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Study of Grid Cascading Faults Based on Second-order Neighbor Load Redistribution Strategy
HU Jinmei, ZOU Yanli, WANG Hongjun, ZHANG Hai
Complex Systems and Complexity Science 2026, 23 (
1
): 1-9. DOI: 10.13306/j.1672-3813.2026.01.001
Abstract
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In this paper, we study the enhancement of network robustness by changing the range of load redistribution in grid cascading faults, and propose a load redistribution strategy considering second-order neighbors. Single-node attack and multi-node attack experiments are conducted on the western United States power grid and Polish power grid using this strategy to analyze the robustness of the network under different load redistribution strategies and different attack methods. Simulation experiments show that the redistribution strategy proposed in this paper shows better robustness and destruction resistance on multiple networks. In addition, a comparative study with the load redistribution strategy that considers higher-order neighbors reveals that there is a saturation effect in the redistribution strategy of the load, and the strategy proposed in this paper is the optimal choice to balance the distribution efficiency and the network robustness.
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A Rumor Propagation Model Considering Rumor-promoter and Rumor-debunker in Online Social Networks
DING Xuejun, HONG Ye, TIAN Yong
Complex Systems and Complexity Science 2025, 22 (
4
): 46-54. DOI: 10.13306/j.1672-3813.2025.04.007
Abstract
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In order to explore the propagation mechanism of rumors in online social networks, this paper takes into account the fact that rumor-promoters and rumor-debunkers coexist and establishes a new SPIDR (Susceptible-Promoted-Infective-Debunked-Recovered) rumor propagation model on the basis of SIR (Susceptible-Infective-Recovered) model, and then the stability of the model is analyzed. The simulation results show that the number of rumor-promoters and rumor-debunkers will affect the spread of rumors. Controlling the number of rumor-promoters will reduce the risk of rumor spreading. In addition, improving the probability of debunking rumors to ignorant people can effectively suppress the spread of rumors. The SPIDR rumor propagation model and simulation results will provide theoretical supports for relevant government departments or organizations to carry out rumor governance.
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Identification of Key Stations and Routes in Urban Metro and Conventional Bus Networks from a Resilience Perspective
SUN Xiaohui, LIU Yi, MI Yumei, LÜ Kai
Complex Systems and Complexity Science 2026, 23 (
1
): 26-36. DOI: 10.13306/j.1672-3813.2026.01.004
Abstract
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Urban Metro and conventional bus carry a significant portion of residents' daily travel services, and their disruption due to sudden incidents often results in widespread and profound impacts. To ensure safe and efficient operation of public transportation, based on complex network theory, a method is proposed from the perspective of structural resilience for identifying key stations and routes of urban metro and conventional bus networks through importance, that is the resilience-based mean square deviation-TOPSIS comprehensive evaluation method. The reliability of this method is respectively verified through the monotonicity of the importance evaluation results, the robustness analysis of different attack strategies, and the comparative analysis of construction timelines. The case study results show that this method can well differentiate each station in the network; when conducting robustness analysis, it can also reflect the characteristic that key stations with greater importance have a larger impact on the overall network performance; the K-means clustering results of the importance of Shenzhen metro lines are generally consistent with the construction timeline. The reliability of this method in identifying key stations and routes is verified comprehensively.
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Efficient Multi-task Visual Perception Model in Autonomous Driving Scenarios
LIU Bohang, ZHAO Qiang, TANG Zhenglin, TANG Yinglong, LI Yeqi
Complex Systems and Complexity Science 2026, 23 (
1
): 130-137. DOI: 10.13306/j.1672-3813.2026.01.016
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To efficiently utilize the hardware computing power of autonomous vehicles, a multi-task perception model OLAD is constructed based on YOLOv5,which can simultaneously achieve traffic object detection, lane lines recognition, and drivable area segmentation. By introducing an improved SPPFCSPC module and redesigning the feature fusion network based on Slim Neck, OLAD enhances feature extraction capabilities, inference speed, and detection accuracy, the loss function is improved by incorporating MPDIoU to boost the accuracy of traffic objects detection. In terms of model performance validation, a comprehensive performance evaluation is conducted by supplementing the self-made domestic road dataset in the BDD100K validation set. The results show that the detection accuracy and speed of OLAD are better than the YOLOP of SOTA; In addition, public road images from different time periods in Suzhou are randomly selected to test the performance of the model on domestic roads. The results show that the perception results of the OLAD model in this paper are more accurate and suitable for domestic roads.
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Electricity Theft Detection Based on Multiscale Residual Attention Network
CHANG Hanyun, CHEN Lishen, QIAN Jianghai
Complex Systems and Complexity Science 2026, 23 (
1
): 37-44. DOI: 10.13306/j.1672-3813.2026.01.005
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Aiming at the shortcomings of traditional power theft detection methods, which only use one-dimensional power, rely on manual features, and have low detection accuracy, an eletricity theft detection model based on multiscale residual attention network is proposed. The model is based on pyramidal convolution to fully extract multi-scale detail features, and introduces hybrid dilated convolutional attention residual network to improve the detection performance. In this paper, the proposed method is experimentally validated using the public dataset of the State Grid, and the results show that compared with the traditional logistic regression, support vector machine, random forest, and other models, the
A
UC
,
M
AP
, and
F
1
score indexes of the proposed model have achieved effective improvement.
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The Evolutionary Characteristics of Cultural Tourism Information Dissemination in the New Media Environment
ZHANG Jie, JIAN Lirong
Complex Systems and Complexity Science 2026, 23 (
1
): 114-122. DOI: 10.13306/j.1672-3813.2026.01.014
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To study the evolutionary characteristics of cultural tourism information dissemination in the new media environment, analyze the impact of blogger promotion and host marketing on potential tourists, apply prospect theory to depict the profit and loss perception of bloggers and hosts in the process of cultural tourism information dissemination, comprehensively use SEIR and evolutionary game theory to construct a cultural tourism information dissemination model, and conduct numerical simulation with scenario cases in Xishuangbanna, Yunnan and Gaochun Old Street, Jiangsu. The research results indicate that, under a single information dissemination, the number of tourists follows an inverted U-shaped curve with the dissemination of cultural tourism information; The dissemination effect of cultural tourism information is positively correlated with the proportion of bloggers who choose communication strategies, the proportion of broadcasters who choose sales strategies, the number of contacts with communicators, the proportion of bloggers in the population, and the number of "fans" of bloggers, but negatively correlated with the duration of dissemination and natural attenuation parameters.
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Evolution of “ Internet + ” Enterprise Innovation Ecosystem Network
ZHOU Qing, LI Yihan, CHEN Wenchong
Complex Systems and Complexity Science 2025, 22 (
4
): 1-7. DOI: 10.13306/j.1672-3813.2025.04.001
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Exploring the evolution characteristics and laws of the “Internet +” enterprise innovation ecosystem network can provide theoretical and model support for the governance of the “Internet +” innovation platform. Based on the scale-free network theory and the network characteristics of the “Internet +” enterprise innovation ecosystem, this paper constructs a system network evolution model with mixed preferential mechanism, and discusses the influence of different preferential mechanisms on the network evolution of the system through simulation analysis.The results show that the importance of non-core enterprises and individual innovators in the “Internet +” system is enhanced, showing a certain degree of decentralization evolution, but it also destroys the connectivity of the network to a certain extent and increases the cost of cooperation between the subjects.
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On the Credit Evolution of Shared Logistics Market Subject Based on Tripartite Evolutionary Game
CHEN Jing, LI Siyu, ZHANG Xiao, WANG Guoyi
Complex Systems and Complexity Science 2025, 22 (
4
): 78-88. DOI: 10.13306/j.1672-3813.2025.04.011
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Considering the credit dilemma in the shared logistics operation, a three-party evolutionary game model of the platform-the logistics resource supplier-the logistics resource demander, and credit margin and reward and punishment policies are designed to explore the formation mechanism of the credit dilemma in the shared logistics platform. The research finds that, credit margin system and punishment for fraudulent transactions have a positive effect on the positive evolution of the system, and are positively correlated with the evolution rate; rewarding honesty and subsidizing complaints can promote the evolution of the system in a positive direction to a certain extent, but exceeding the threshold will increase the burden of the shared logistics platform; compared to rewarding integrity, punishing fraud has a more significant impact on the evolution of the system towards a positive direction, so the strategy of punishment first and reward second is more suitable for the healthy and sustainable development of shared logistics.
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Location and Routing Optimization of Logistics Distribution Center Based on Bi-level Programming
WAN Mengran, YE Chunming
Complex Systems and Complexity Science 2025, 22 (
4
): 118-124. DOI: 10.13306/j.1672-3813.2025.04.015
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To improve the efficiency of urban logistics and reduce road congestion, a bi-level programming model is adopted to solve the problem of logistics distribution center location and path optimization. The upper-level model utilizes an improved Adaptive Immune Optimization Algorithm (IAIA) to determine the distribution center locations that minimize costs. Meanwhile, the lower-level model aims to minimize vehicle travel time considering road congestion, improving the Ant Colony Algorithm (IACA), and considering the influence of actual travel speeds on pheromone concentration updates. Through experiments with designed logistics distribution test cases, it is validated that the bi-level programming model, the improved Adaptive Immune Optimization Algorithm, and the enhanced Ant Colony Optimization Algorithm are effective approaches for solving logistics distribution center location and route optimization problems.
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A Convergence Iterative Method for the Evolution of Complex Networks Based on Adjacency Matrices
MOU Qifeng, LI Xiaoqian
Complex Systems and Complexity Science 2026, 23 (
1
): 79-86. DOI: 10.13306/j.1672-3813.2026.01.010
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To efficiently address the continuous splitting and recombination of complex network topological structures and reduce computational resource consumption, a method called adjacency matrix fusion iteration is proposed. The complex network aggregation is achieved through the fusion of adjacency matrix row-column vectors, the steps and forms of network evolution fusion and splitting iteration are defined, and empirical analysis is carried out as an example of constructing a flight guarantee network. Finally, the fusion splitting process of the directed network is simulated, and time and space complexity indicators are introduced to verify the effectiveness of the method. The results show that the proposed method is consistent with the evolutionary generation process of the empirical network topology, and its arithmetic complexity is lower than that of other methods, which is especially suitable for the study of directed dense networks.
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Fixed-time Control of Nonlinear Systems with Full State Constraints Systems
GUO Qing,cAI Mingjie, WANG Baofanga,b
Complex Systems and Complexity Science 2026, 23 (
1
): 153-159. DOI: 10.13306/j.1672-3813.2026.01.019
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A novel nonlinear mapping is introduced to address the fixed-time control problem of nonlinear systems with full state constraints, and a fixed-time control design method is proposed using the nonlinear mapping method. Firstly, We establish a mathematical model of a nonlinear system with full state constraints; Secondly, by combining time-varying state constraints and using nonlinear mapping techniques, the system with existing constraints is transformed into a corresponding unconstrained system; Then, a fixed-time control law based on backstepping is designed using a radial basis function neural network; Finally, the stability of the system is demonstrated using Lyapunov theory, and the effectiveness and feasibility of the proposed control method are verified through specific simulation examples.
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Weighted Directed Network Evaluation Algorithm Based on Propagation Model
ZHANG Xiruo, LIAO Yuan, PENG Jiaqin, YANG Yuhang, HUANG Liya
Complex Systems and Complexity Science 2026, 23 (
1
): 10-16. DOI: 10.13306/j.1672-3813.2026.01.002
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To investigate node importance in the extensive weighted directed networks in real-world scenarios, this paper proposes the Cross
K
-Propagation Number (CKPN) algorithm, which is a node evaluation algorithm for weighted directed networks based on propagation models. This algorithm analyzes node information from both local and global perspectives, examines the interaction between nodes under different propagation orders and adjusts the contribution allocation of the in-degree and out-degree in the directed network. ARPA network, WSIR model and deliberate attack model are used to verify the effectiveness of the proposed method. The results show that the CKPN algorithm considers the information comprehensively and the evaluation results are detailed. It has good effect in large-scale networks and is more accurate than the traditional algorithm that only considers the network topology.
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Granger Causality-based Method for Determining Objective Weights of Landslide Mechanism Network
ZHANG Haochun, KOU Boxiao, ZHANG Taijie, TANG Zhihui
Complex Systems and Complexity Science 2025, 22 (
4
): 63-70. DOI: 10.13306/j.1672-3813.2025.04.009
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Existing studies have shown that landslide is a complex geological phenomenon with multi-factor causation, and the weighted complex network is an important tool to study the complex causation mechanism, however, the existing weighting method cannot reflect the characteristics of the interactions between landslide causation, and it is necessary to propose a new quantitative method to assign weights to the connecting edges. Based on Granger causality analysis, this paper proposes a quantification method based on objective data weights to objectively assign weights to the strengths of interaction between landslide causal factors. Different objective quantification models were constructed to consider the linear or non-linear relationships among causal factors; and the effectiveness of the method was verified based on the causal data of precipitation, vegetation, surface runoff and other causal in the landslide mechanism network with scalability. The results show that the weighted quantification models can be based on objective causal time series and realise the dynamic assignment of the causal factors,which lays a solid foundation for quantitative research based on weighted complex networks.
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Operational Effectiveness Analysis of Maritime Counter Unmanned Cluster Based on Agent Modeling
FAN Huijin, CHEN Qinghua, WU Yinhua
Complex Systems and Complexity Science 2025, 22 (
4
): 89-98. DOI: 10.13306/j.1672-3813.2025.04.012
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In order to study the operational effectiveness of maritime counter unmanned cluster under the background of joint operation, the operational agent modeling method is adopted to carry out the analysis and research on the operational effectiveness. Focusing on the maritime counter unmanned cluster operation the modeling process and basic structure of combat agent are designed, and the counter unmanned cluster operational effectiveness model is constructed from the establishment of the effectiveness index system, individual agent modeling and main state change, and the intrinsic mechanism model of key agents is given. A specific operational design and a operational simulation experiment system based on Anylogic are designed to examine the effectiveness, feasibility and superiority of the modeling method. The results show that the modeling method can better support the analysis and assessment of maritime counter unmanned cluster operational effectiveness, and derive the key influencing factors of combat effectiveness.
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Evolutionary Mechanism of Green Technology Innovation Network in the Yellow River Basin
XIANG Bowen, XU Ying, XU Gaofeng
Complex Systems and Complexity Science 2026, 23 (
1
): 17-25. DOI: 10.13306/j.1672-3813.2026.01.003
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To study the evolutionary mechanism of green technology innovation network in the Yellow River Basin, this study, using social network analysis and the index random graph model, analyzed the evolution characteristics and mechanisms of green technology innovation networks in the Yellow River Basin from 2011 to 2019. The findings are as follows: The scale and cooperation intensity of the innovation network continuously increased, with small-world and scale-free properties remaining significant, but connection closeness decreased. In the upstream Yellow River Basin, it transitioned from a single-core innovation cluster centered around Xi'an in Phase One (2011-2013) to three innovation clusters: Qinghai, Ning-Shaan-Yu, and Gan-Inner Mongolia-Jin in Phase Two (2017-2019). In the downstream region, single-core clusters around Jinan and Qingdao in Phase One integrated into the Shandong Peninsula Urban Agglomeration innovation cluster in Phase Two. Organizational and cultural proximity facilitate intercity innovation but also amplify provincial and cultural "boundary effects." City clusters and basin proximity did not create "boundary effects," but policy and basin proximity did not promote intercity cooperation. Geographic and technological proximity, city scale, innovation levels, and green innovation levels positively impact intercity innovation. This study's "proximity-boundary" analysis framework contributes to understanding innovation network impact mechanisms and provides theoretical and policy support for optimizing the green innovation system in the basin.
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Identification of Important Nodes in Complex Networks Based on Node Influence Factor and Contribution Factor
SUN Wenjing, YU Lufen, PAN Wenlin, LAN Chunjiang
Complex Systems and Complexity Science 2026, 23 (
1
): 87-95. DOI: 10.13306/j.1672-3813.2026.01.011
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For high aggregation networks, we proposed a new method KEC for identifying important nodes in complex networks, which considered both the local information of nodes and neighbors, that is, the influence factors, and the contribution degree of neighbors to the influence of nodes, and put forward the contribution factor. In eight real networks, the method used the SIR model and deliberate attack experiments to analyze the performance of KEC and six commonly used centrality. Finally, the method used the Kendall-tau correlation coefficient to analyze the correlation between the values of nodes calculated by KEC and six commonly used centrality. The results show that it is effective for KEC to identify influential node sets and improve the destruction resistance of networks, and the Kendall-tau correlation coefficients between KEC and six commonly used centrality are almost positively correlated in eight real networks, which shows that it is feasible for KEC to identify important nodes in complex networks.
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Impact of Bidirectional Immunization on Epidemic Spreading in Complex Networks
HAN Shixiang, YAN Guanghui, PEI Huayan
Complex Systems and Complexity Science 2025, 22 (
4
): 55-62. DOI: 10.13306/j.1672-3813.2025.04.008
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In epidemic prevention and control efforts, the rational allocation of medical resources has consistently been a focal point of attention for professionals in the field. In order to investigate the practical effectiveness of various immune measures in epidemic prevention during the process of pandemic spread, this study introduces an infectious disease model within complex networks that considers bidirectional immune interventions. Through theoretical analysis and numerical simulations of the model, we delve into a detailed discussion on the impact of immune measures targeted at different population groups on the transmission of the virus. In the theoretical analysis, the stability of the disease-free equilibrium point in the model is examined through the incorporation of the basic reproduction number analysis. In numerical simulations, the impact of bidirectional immunization and population mobility on the spread of infectious diseases is scrutinized through Monte Carlo simulations within the context of complex networks. Simulation results indicate that, compared to enhancing the recovery rate of infected individuals, increasing the immunization rate among susceptible individuals can more effectively reduce the scale of infectious diseases.
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Robustness Analysis of the World Airline Network Considering Multiple Variables
HU Zuoan, YANG Jianghao, DENG Jincheng
Complex Systems and Complexity Science 2026, 23 (
1
): 60-69. DOI: 10.13306/j.1672-3813.2026.01.008
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Due to the inadequacy of using a single indicator to evaluate the air network robustness, it is necessary to further consider multiple indicators and their core variables to propose a comprehensive evaluation method, in order to analyze and evaluate the network robustness comprehensively, this paper considered multiple variables such as the number of remaining nodes, the number of neighbor links, and the shortest path, to establish a comprehensive robustness evaluation index. Set up four failure scenarios and simulated them on the four networks. The simulation results show that, under random failure, the World-Airline Network has the highest robustness among the four networks, and its comprehensive robustness index only drops to zero after almost all nodes fail; under three malicious failure scenarios, the World-Airline Network fails to maintain robustness when a small number of nodes fail, and collapses completely when about 20% of nodes fail; under three malicious failure strategies, the comprehensive robustness curves of the World-Airline Network are basically consistent, which proves the universality of this comprehensive robustness metric.
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Adaptive Sliding Mode Fault-tolerant Control for Chaotic Systems with Network Faults
LUO Sunxiaoyu, ZHU Kexin, CHEN Tianzhi, ZHAO Fuyu, ZHAO Liang
Complex Systems and Complexity Science 2025, 22 (
4
): 154-160. DOI: 10.13306/j.1672-3813.2025.04.020
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A novel adaptive sliding mode control strategy is proposed for a class of chaotic systems with the signal attenuation, network degradation, and nonlinear coupling characteristics, to solve the problem of robust fault-tolerant control and synchronization of chaotic systems. An integral sliding manifold for chaotic synchronization is presented, and an adaptive law is designed to estimate the control gain, and the updated control gain and integral gain are used to construct an adaptive sliding mode controller. Based on the Lyapunov stability theory, it is proved that the designed controller can ensure the asymptotic synchronization of chaotic systems with faults and perturbed couplings. The effectiveness and applicability of the proposed method are verified by the numerical simulation, which provides a new idea for the robust fault-tolerant control and synchronization of chaotic systems.
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Integrating Local Relationships and Entities in Knowledge Graph Completion Model
GAO Rui, SUN Gengxin, BIN Sheng
Complex Systems and Complexity Science 2026, 23 (
1
): 138-145. DOI: 10.13306/j.1672-3813.2026.01.017
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Given that the majority of existing knowledge graph completion methods adopt an independent processing approach for triplets, overlooking the varying contributions of neighborhood relations and entities to the central entity,this paper introduces a graph neural network model called REGNN that integrates neighborhood relations and entities. In this model, feature information from relations and entities within the neighborhood is incorporated into the central entity′s update, enriching the representation of the central entity through the aggregation of entity and relation features. Experimental results demonstrate that, in comparison to traditional graph neural network models, REGNN model achieves improvements of 3.3% and 1.5% in terms of the MMR and Hits@10 metrics on the FB15K-237 dataset, and improvements of 1.4% and 3.6% on the WN18RR dataset, thus validating the effectiveness of REGNN model.
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Urban Economic Flow Structure and Economic Energy Level Measurement from the Perspective of Multiplex Networks
SHI Yan, ZHANG Zili, ZHAO Xuejun
Complex Systems and Complexity Science 2026, 23 (
1
): 96-103. DOI: 10.13306/j.1672-3813.2026.01.012
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To promote the coordinated and high-quality development of China's economy, this study combines the theory of flow-based economy and multiplex network analysis methods to construct a network model of material, capital, and technology information flow among cities. The entropy-based multi-attribute node importance measurement method is applied to propose a new framework for measuring the level of urban economy. Research shows that urban network structure is closely related to changes in macroeconomic conditions. The output results of the constructed economic level measurement model are consistent with authoritative survey reports, thus proving its effectiveness. Further studies reveal notable urban economic disparities across China's regions, with the east and the Yangtze River Delta in the lead. Positive trends emerged in the west and northeast due to policy guidance, but the central and Bohai Economic Circle still need more policy support. The flow of technological information is crucial for the upgrading of economic levels in economically developed regions. In contrast, the growth of levels in underdeveloped regions relies more on new capital investment.
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High-order Networks Robustness Analysis Based on Self-adaptive
YU Wenqian, MA Fuxiang, CHEN Yang, MA Xiujuan
Complex Systems and Complexity Science 2025, 22 (
4
): 15-23. DOI: 10.13306/j.1672-3813.2025.04.003
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This paper considers the multivariate coupling relationship between nodes, combines high-order structures and actual load redistribution situations, proposes four self-adaptive load redistribution strategies, and analyzes the robustness of three types of synthetic higher-order networks, common networks (graphs), and real higher-order networks. Simulation experiments show that the scale of higher-order networks is positively correlated with their robustness. At the same time, different higher-order structures and self-adaptive load redistribution methods have different impacts on the robustness of higher-order networks. In addition, the self-adaptive load redistribution methods proposed in this paper are also applicable to common networks (graphs) and real higher-order networks.
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Disturbance-Compensation-Based Containment Control for Multiple Discrete-Time Euler-Lagrange Systems
GUO Xinchen, SONG Chuanming, LIANG Zhenying
Complex Systems and Complexity Science 2026, 23 (
1
): 123-129. DOI: 10.13306/j.1672-3813.2026.01.015
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The containment control problem for multiple discrete-time Euler-Lagrange (EL for short) systems is studied in this paper. Firstly, the discrete-time EL system is transformed into a discrete-time second-order nonlinear system through the famous Euler’s first-order approximation method, and a local disturbance identifier is designed to estimate the compound disturbance for each EL system. Meanwhile, the tracking error dynamics are obtained by designing a state feedback controller involving both the available nonlinear term and the compensation of disturbances. Then, the finite-time boundedness and exponential ultimate boundedness of tracking errors are guaranteed, respectively, by selecting suitable controller gains. Finally, the effectiveness of the proposed control scheme is further verified by a numerical simulation of a group of two-link robotic arm systems.
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Routability Prediction for FPGA Design Based on Complex Networks and Attention Mechanism
NIE Tingyuan, WANG Yanwei, NIE Jingjing, LIU Pengfei
Complex Systems and Complexity Science 2026, 23 (
1
): 53-59. DOI: 10.13306/j.1672-3813.2026.01.007
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FPGA routability prediction is of great significance for solving the optimization of physical design. We propose an FPGA routability prediction model based on complex networks and CBAM-CNN. During the placement phase, we extract circuit features and complex network features related to circuit congestion and map them to RGB images. We introduce an attention mechanism to enhance the importance of features. The experimental results show that the prediction accuracy is 98.03%, precision is 98.3%, sensitivity is 98.3%, specificity is 97.67%, and the Matthews correlation coefficient is 93.75%. The importance of complex network features in FPGA routability prediction is ranked in order of degree, strength, eigenvector, and betweenness. This proves the effectiveness and importance of complex network features in predicting FPGA routability.
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On the Cooperative Governance Behavior of Internet Rumors Based on Differential Games
YANG Renbiao, YIN Chunxiao
Complex Systems and Complexity Science 2025, 22 (
4
): 145-153. DOI: 10.13306/j.1672-3813.2025.04.019
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The spread of rumors in the online environment can disrupt social order. Based on the perspective of a cooperative game, this paper explores the collaborative governance behavior between government departments and social platforms in the process of rumor dissemination and conducts an in-depth analysis by combining with the rumored case of "3.21 China Eastern Airline MU5735 Flight Accident", and finally verifies it through simulation. The results show that, firstly, the government and platform have the highest willingness to participate in the collaborative game, and in the Stackelberg master-slave game, the platform's willingness to collaborate is significantly improved compared with that of the Nash non-cooperative game, but the government's willingness does not increase; secondly, the government and the platform have the highest overall benefit from the collaborative game, followed by the Stackelberg master-slave game and the Nash non-cooperative game. game is the lowest; finally, only when the allocation coefficient between the government and the platform is within a certain range, the synergistic behavior of both parties can reach the Pareto optimal state.
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Influence of ESG on Contagion of Credit Risk Based on Scale-free Networks
LIU Xuejuan, ZHANG Jingyi, CAO Hui
Complex Systems and Complexity Science 2025, 22 (
4
): 8-14. DOI: 10.13306/j.1672-3813.2025.04.002
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In order to discover the influence of ESG score on the evolution of enterprise-associated credit risk, this paper proposed a contagion model of enterprise-associated credit risk considering ESG score based on the mean field theory of heterogeneous network, and the simulation is carried out based on the BA scale-free network. The study found that improving the ESG score is important for controlling the contagion of associated credit risk. Increasing the ESG score of such enterprises when their influence is weak is beneficial for suppressing the number of enterprises affected by associated credit risk. Increasing the ESG score of such enterprises when their influence is large is favorable for reducing the speed of associated credit risk contagion. Additionally, increasing the proportion of the ESG score in corporate credit evaluation indicators is also beneficial for controlling the credit risk contagion.
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Robustness Optimization Strategy for Networks Based on Peripheral Nodes of Communities
PAN Wenxiang, LI Dongyan, SUN Sixiang, TONG Ning
Complex Systems and Complexity Science 2026, 23 (
1
): 70-78. DOI: 10.13306/j.1672-3813.2026.01.009
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To improve the efficiency of the network robustness optimization strategy, the impacts of several major types of optimization strategies on the structure of urban infrastructure networks were analyzed. A strategy called Community Periphery nodes link Addition (CPA) was proposed to optimize network robustness. This strategy uses the Girvan-Newman algorithm to determine the community structure of complex networks, regards each community as a network, uses the K-shell algorithm to determine the position of the network center within each community, identifies the node within each community which is least affected by the network center as the community periphery node, and establishes edges based on these periphery nodes. The experimental results based on the real infrastructure network and BA scale-free network model demonstrate that compared with classical strategies,such as random edge addition strategy, low-degree addition strategy, low-betweenness addition strategy, and algebraic connectivity addition strategy, the CPA strategy generally achieves higher efficiency in improving network robustness.
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Fault Tolerance Consistency of Nonlinear Heterogeneous Multi-agent Systems Based on Event Triggering
WANG Jun, CAI Xueqiang
Complex Systems and Complexity Science 2025, 22 (
4
): 99-108. DOI: 10.13306/j.1672-3813.2025.04.013
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Aiming at actuator faults and external disturbances in nonlinear heterogeneous multi-agent systems, a fault tolerance consistency algorithm based on event triggering is proposed to ensure system consistency. A trigger function based on state error is designed for the follower. The agent only triggers the event in a certain case, updates and transmits the sampled information. By synthesizing model transformation, matrix theory and Lyapunov stability theory, the sufficient conditions for the system to reach agreement are obtained, which ensures the stability of the system. The control gain matrix is solved by linear matrix inequality (LMI) based on Lipschitz and norm bounded conditions when nonlinear elements are considered. The feasibility and effectiveness of the proposed method are verified by Matlab simulation experiments.
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Containment Control of Second-order Multi-agent Systems with Exogenous Disturbance Under Intermittent Measurement
MENG Weichen, WANG Qingzhi, LIU Yongchao, FU Baozeng
Complex Systems and Complexity Science 2025, 22 (
4
): 109-117. DOI: 10.13306/j.1672-3813.2025.04.014
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In order to solve the containment control problem of second-order multi-agent systems under intermittent measurement and with exogenous disturbances, a novel disturbance observer for each agent is presented initially. Then, based on the Lyapunov function method and linear matrix inequality technique, sufficient conditions are established to achieve containment control for second-order multi-agent systems with exogenous disturbances under intermittent measurement. Finally, when exogenous disturbances vanish, the less conservative corollary is given. The simulation results show that the control protocol designed by the sufficient conditions can still play an effective role under intermittent measurement and with exogenous disturbances, and that the measurement time calculated by the corollary is smaller.
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State Estimation of Boolean Control Networks Based on Control Inputs and State-flipped
XING Qian, YANG Junqi, WANG Shangkun
Complex Systems and Complexity Science 2026, 23 (
1
): 146-152. DOI: 10.13306/j.1672-3813.2026.01.018
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In order to solve the state estimation problem of Boolean control networks, control inputs and state-flipped control are used in this paper. First, relying on the control inputs, the Boolean control network is transformed into a Boolean network, and then the state estimation problem of Boolean control network is studied based on the control inputs and outputs. Second, the state-flipped control is introduced to the system when the elements of the set of output-dependent state estimation are not unique, and a sufficient condition is proposed to realize the reachability of the target state. Third, all states in the output-dependent state estimation set are simultaneously flipped to the target state by designing an algorithm to calculate the joint control pair sequences, and further the state estimation of the Boolean control network is realized. Finally, it is shown through examples that the research method enables state estimation of Boolean control networks.
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Stability Analysis of Fractional Order Ecological Epidemiological Model with Stage Structure
DOU Zhongli
Complex Systems and Complexity Science 2025, 22 (
4
): 133-138. DOI: 10.13306/j.1672-3813.2025.04.017
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In this paper, the stability of a fractional order ecological epidemic model with stage structure and predator delay time during pregnancy was studied. By calculating the characteristic roots of the model and using Routh-hurwitz criterion, it is obtained that the predator extinction equilibrium point, disease-free equilibrium point and endemic equilibrium point are locally asymptotically stability, a sufficient condition for the generation of Hopf bifurcation near the endemic equilibrium is obtained. At the same time, the influence of fractional order on the bifurcation point decreases is discussed, and it is found that the bifurcation point of the system decreases as the order increases. Finally, the validity of the theoretical conclusion is verified by numerical simulation.
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Complexity Prediction of Air Traffic Interdependent Network Based on ICA-LSTM
QI Yannan, WANG Xintong, WU Zuoyu
Complex Systems and Complexity Science 2025, 22 (
4
): 37-45. DOI: 10.13306/j.1672-3813.2025.04.006
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In order to address the air traffic complexity prediction problem, an ICA-LSTM prediction model is established by constructing the air traffic interdependent network and extracting the nonlinear spatiotemporal dynamic characteristics of air traffic data, which improves the accuracy of prediction. Firstly, based on the complex network theory, taking aircraft and control sectors as the research objects, a flight-control air traffic interdependence network was established. Secondly, network characteristic indexes were selected from the three dimensions of “point-line-surface”, and the common factors of these indexes were extracted using factor analysis method, and an air traffic complexity model was established. Finally, a spatiotemporal series of air traffic data is constructed, the independent component analysis (ICA) is used to extract data sample characteristics, and an ICA-LSTM air traffic complexity prediction model is established. ADS-B operational data from the Beijing terminal area is used for verification, and the results show that the model can effectively predict air traffic complexity. Moreover, compared with traditional LSTM and SVM models, the ICA-LSTM model has higher prediction accuracy.
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Dynamic Scheduling for Mixed-batch Equipment Based on an Improved Memetic Algorithm
HUANG Jindian
Complex Systems and Complexity Science 2025, 22 (
4
): 71-77. DOI: 10.13306/j.1672-3813.2025.04.010
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To enhance the processing efficiency of vacuum heat treatment workshop with the goal of minimizing makespan, this paper constructs a mathematical model for mixed-batch scheduling that considers incompatible families of jobs. An improved memetic algorithm is proposed for dynamic scheduling of equipment. Typical local search strategies for batch scheduling are analyzed. The heuristic algorithms and memetic algorithms based on greedy and hill-climbing strategies are used as benchmark algorithms. The scheduling results of various algorithms are compared with the lower bound of the problem, and large-scale simulations show that the newly designed improved memetic algorithm outperforms other algorithms in a multi-job family environment, thus effectively improving scheduling performance.
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Improving Network Controllability: a Graph Convolutional Network Based Approach
LU Xinbiao, LIU Zecheng, CHEN Guiyun, YANG Tieliu, GAO Xing
Complex Systems and Complexity Science 2025, 22 (
4
): 24-28. DOI: 10.13306/j.1672-3813.2025.04.004
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In order to improve network controllability, a network controllability improvement method based on graph convolutional neural network is proposed, in which a graph convolutional network is first trained to select appropriate nodes, and then edges are randomly added between these selected nodes. Numerical simulations are carried out on two representative complex network models. Compared with the traditional method in which edges are added randomly between all nodes, the proposed method greatly reduces the number of added edges, which is more efficient.
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Scheduling Optimization of Railway Container Terminals with "Rail Crane-common Bay"
LIU Fenghui, ZHANG Jihui
Complex Systems and Complexity Science 2025, 22 (
4
): 125-132. DOI: 10.13306/j.1672-3813.2025.04.016
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For the scheduling problem of railway container terminal with fixed operating range of rail cranes, the K-means clustering algorithm is used to divide the operation tasks into direct unloading tasks and indirect unloading ones. In order to fully utilize the idle container space of the yard, a common bay is selected as the relay point to divide the working area of the rail cranes, and dynamic adjustment rules for the common bay are designed to obtain the optimal operating area of the rail cranes. A mixed integer programming model with the goal of minimizing the completion time is established, and a method to determine the interference between two rail cranes at the relay point is given. A solution algorithm combing genetic algorithm and ant colony algorithms is designed, and the pheromone mechanism is added to generate the solution to improve the quality of the solution; Different grouping mechanisms are proposed to update the population for avoiding to fall into local optimum. The numerical simulation experimental results show that the proposed method has significant advantages in solving such problems. For a fixed rail crane and truck configuration and the given task, compared with the "rail crane truck" and rail crane flexible scheduling modes, the "rail crane common bay" operation mode has a shorter completion time.
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Causation Analysis for Hazardous Materials Transportation Accident Based on Meta-network Model
REN Cuiping, ZHANG Jiaqian
Complex Systems and Complexity Science 2026, 23 (
1
): 45-52. DOI: 10.13306/j.1672-3813.2026.01.006
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In order to reveal the key factors of hazardous materials transportation accidents and the structural relationship between factors, a new node system is established with agent, behavior, consequence, organization, environment and event as elements, using the meta-network model, combined with the characteristics of hazardous materials road transportation. Taking the major transportation explosion accident of ‘6.13’liquefied petroleum gas tank truck in Wenling, Zhejiang Province as an example, constructed the meta-network of hazardous materials transportation accidents and analyzed the structural characteristics and strike strategies of the network. It is found that the network of hazardous materials transportation accidents presents the characteristics of sparse network. The key strike effect with the closeness centrality is the best.
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Incentive Mechanisms for Green Transformation of Buildings Based on Communication Dynamics
FAN Chunmei, LI Xiaoyue
Complex Systems and Complexity Science 2026, 23 (
1
): 104-113. DOI: 10.13306/j.1672-3813.2026.01.013
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To explore the mechanism of local government incentive policies on the supply and demand of green buildings, the study constructs the SEIR evolutionary game model based on the theory of evolutionary game and communication dynamics, exploring the game relationship between developers and local governments and the diffusion of green buildings among consumers under the different behavioral decisions of the two players. Research shows that green awareness exerts the most significant influence, and the diffusion of green buildings is maximized at the development stage as the level of stakeholders′ green awareness increases. In addition, the influence of local government behavior on green building diffusion is more significant than that of developers, and the incentive effect of subsidy policies is better than tax incentives.
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Study of Early Warning Signals for Disease Re-emergence Considering Population Behavior
WANG Xueqing, ZHOU Rui, ZHAO Jijun
Complex Systems and Complexity Science 2025, 22 (
4
): 139-144. DOI: 10.13306/j.1672-3813.2025.04.018
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This study aimed to explore the performance of Early Warning Signals (EWS) in predicting the re-emergence of infectious diseases under the influence of vaccination behavior in dynamic systems. First, we established an infectious disease model considering population behavior. Then, we used the model simulation data to calculate different statistical indicators, including mean, variance, autocorrelation coefficient, incremental variance, skewness, and residuals, which will be used as EWS. Finally, we used the Receiver Operating Characteristic curves(ROC)to evaluate the performance of these indicators. Autocorrelation coefficient, variance, mean, and incremental variance demonstrated favorable performance. The results demonstrate the effectiveness of EWS in detecting the transitions of infectious disease systems and hold particular significance in the study of early warning signals for disease outbreaks.
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Exploring the Factors of Tie Dissolution of Innovation Cooperation in Integrated Circuit Industry
LIU Xiaoyan, ZHAO Xiyu, SHAN Xiaohong, XIE Guisheng
Complex Systems and Complexity Science 2025, 22 (
4
): 29-36. DOI: 10.13306/j.1672-3813.2025.04.005
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Exploring the factors that affect the tie dissolution of innovation cooperation in IC industry can realize the early warning of tie changes and improve the stability of innovation cooperation network.. Drawing on the embeddedness theory, this study constructs a model for analyzing the factors influencing the dissolution of ties within the innovation cooperation network of the integrated circuit industry, incorporating the dimensions of relational heterogeneity and relational embeddedness. Machine learning algorithms such as GBDT (Gradient Boosting Decision Tree) and RF (Random Forest) are employed to identify the key factors contributing to ties dissolution. The research findings indicate that as the scale of the integrated circuit industry's innovation cooperation network expands, ties dissolution becomes more apparent. The intensity of ties is identified as the fundamental factor influencing relationship dissolution. Regional heterogeneity and capability heterogeneity are identified as critical factors affecting tie dissolution. When assessing the risk of partnership dissolution, it is necessary to comprehensively consider tie intensity, regional heterogeneity, capability heterogeneity, and constraint coefficients.
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A Method for Calculating Node Similarity in Hypernetworks Based on Higher-order Distance Distribution
YANG Yusheng, GUO Lei, FAN Jingyan, HU Feng
Complex Systems and Complexity Science 2026, 23 (
3
): 1-10. DOI: 10.13306/j.1672-3813.2026.03.001
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To address the limitations of traditional hypernetwork node similarity methods in capturing higher-order topological structures, a method for calculating node similarity in hypernetworks based on Higher-order Distance Distribution (HDDNS) is proposed. The method generates higher-order distance distributions for nodes and employs Jensen-Shannon divergence to quantify inter-node similarity. To evaluate its effectiveness, this study conducted systematic experiments on three synthetic hypernetworks and five real-world hypernetworks, comparative analysis with five existing methods demonstrates that HDDNS exhibits superior performance in two key evaluation dimensions: mutual similarity metrics and propagation influence, the results indicate that HDDNS enables more precise and efficient computation of inter-node similarity.
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