To further investigate the regulatory role of coupled time-delay on the modes of discharge activity in a half-center oscillator (HCO), based on the Hindmash-Rose (HR) neuronal model, the DHCO (delayed HCO) model with bursting behavior is constructed. By calculating phase difference between clusters of the bursting, dynamical evolution of the DHCO nervous system is studied with time-delay regulation. The DHCO system presents in-phase and anti-phase bursting oscillations in different parameter spaces. The synchronization transition of the bursting is determined under time-delay controlling. The results show that the DHCO model, regarded as the functional unit of the CPG (Central pattern generator) system can generate and switch multiple locomotion gaits by adjusting time-delay.

The current research on supply chain risk propagation has limitations in the description of enterprise status setting and the relationship between enterprises. A cellular space is mapped to represent the supply chain network, fully considering the differences in operating capabilities of node enterprises under interruption risks and the mutual influence of neighboring cells. The improved risk transmission rule and a simulation model based on cellular automata and SEIRD infectious disease models are constructed. According to the results of multi-scenario simulation and research expansion, the potential reasons for the advancement of supply chain network disruption risk propagation process are analyzed, as well as the influence of market heat, market competition degree, risk early warning and control, and government macro-control on the propagation trend. The research conclusions can provide strategic reference for supply chain disruption risk management decision-making.

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.

In order to discover new chaotic systems, the generalized Lorenz-Stenflo chaotic system is constructed based on the Lorenz-Stenflo chaotic system by adding the disturbance parameters. The basic chaotic characteristics of this system are analyzed by means of the dissipation, equilibrium point and stability, bifurcation diagram and Lyapunov exponential spectrum. Based on Lyapunov stability theory, the analytical expression of the global exponential attractive set of the system is given. The global exponential synchronization is achieved by adding linear feedback control to two generalized Lorenz-Stenflo systems by using the estimator of system solution boundness. Finally, the numerical simulation of the synchronization process is carried out, and the computer simulation results confirm the theoretical feasibility of global exponential synchronization.

This paper investigates the output consensus control problem of multi-agent systems with unmeasurable states under performance constraints. Firstly, the fuzzy logic system is used to approximate the unknown nonlinear function existed in the controlled system, and the adaptive fuzzy observer is introduced to estimate the unmeasurable state. Secondly, a filter whose filtering error can be ensured to converge in a fixed time is designed, which effectively avoids the “complexity explosion” problem in the distributed controller design process. In order to further realize better transient and steady-state performance of the system, a finite-time prescribed performance function that does not depend on the initial conditions of the error is designed. By designing an appropriate barrier function, the relationship between the error performance constrained system and the unconstrained system is established. Combining backstepping and fixed-time dynamic surface techniques, a consensus control scheme with finite-time prescribed performance is proposed. This scheme not only ensures that the output of each follower and the output of the leader finally reach synchronization, but also the consensus error converges to the specified constraint range in a finite time. Finally, the effectiveness of the proposed method is verified by numerical simulation.

Aiming at the problem of conflicting lane changing behaviors of intelligent connected vehicles, a vehicle lane changing decision model based on the game theory is proposed. Firstly, the scenarios of major conflicts occurring in the process of vehicle lane changing are classified, and the lane changing game model is proposed. Then the time difference to collision (TDTC) is introduced, and the speed gains, safety gains and efficiency gains are established as the game payoff function. Besides, the decision-making mechanism is established to improve the efficiency of vehicle lane-changing decision-making. Simulation experiments and comparative analysis of the safety and feasibility of two decision models in conflict situations are conducted using MATLAB software, which includes the proposed lane-changing game decision-making model and the mixed-strategy gaming decision making model. The results show that the proposed lane-changing game decision-making model has higher decision-making efficiency and safety.

Aiming at the difficulty of tracing Internet rumors, a Node Feature-Enhanced Traceability Model (NFETM) is proposed based on information carrier model and in-depth mining of user characteristics. This paper aims to use deep learning method to obtain high-order multi-scale features of information nodes (high-order neighbors, neighbor states, different state connection structures), and combine SEIR propagation mechanism to learn node states into information sources (I states) and non-information sources (S, E, R states). Firstly, multiple node centrality indexes are used to expand and enrich node characteristics. Secondly, an anti-noise enhancement module is used to reconstruct the expanded node features, and dynamically learn the features of the node itself and its first-order neighbors. Thirdly, the metric learning method is used to adjust the node feature space, so that the distance between nodes in the same state is reduced, so as to distinguish the categories and characteristics of nodes. Finally, the multi-dimensional features of nodes are fused and classified to determine the information source. The experimental results show that the proposed model achieves relatively good results in both the simulated generation network and the real network.

To study the strategic choices of PAID’s (Poverty-Alleviation-based Industry Development) participants in poverty-stricken areas, this paper constructs a tripartite evolutionary game model of poverty alleviation enterprises, impoverished households, and local governments, based on the assumption of bounded rationality. Combining with practical cases, it explores the evolutionary stability strategies of participating entities in different contexts. The result shows that there exists a unique stable equilibrium solution in a tripartite game system, and when the expected returns of the enterprise exceed a certain threshold, it can stimulate the enthusiasm of the participating entities. The proportion of labor force in poverty-stricken areas reflects the key driving role of the implicit poverty alleviation chain. The establishment of a reasonable reward and punishment mechanism by the government helps to promote the evolution speed of enterprise strategy selection. The government’s establishment of a reasonable reward and punishment mechanism helps to promote the evolution speed of enterprise strategy choices, and the three parties work together to promote the sustainability of PAID.

In order to explore the impact of intelligent inventory decisions trained by deep reinforcement learning algorithms on the dynamic evolution of supply chain systems, this paper considers the perspective of real-world decision makers and utilizes system dynamics modeling to reproduce the logical structure of a four-order supply chain model constructed using deep reinforcement learning. The decision results are visualized to assess their impact on the system. The experiments illustrate that the algorithm can make better ordering decisions based on the setting of its objective function, but it fails to achieve the lowest cost for the members who apply the algorithm synchronously. The evolutionary process reveals that the Sterman strategy has the role of maintaining the stability of the system during dynamic evolution; establishing a reasonable number of iterations helps to obtain a lower total supply chain cost.

To reveal the transmission characteristics of respiratory infectious diseases clustering epidemic and explore the crucial role of network science in infectious disease control, we constructed and analyzed transmission networks for clustering epidemic, social relationship transmission networks, directed weighted bipartite networks between two gender-based age groups, and their corresponding null model networks based on structured post-epidemiological investigation data. The results indicate that by extracting key indicators from epidemiological investigations, constructing transmission networks, and analyzing them, it is possible to accurately focus on epidemiological characteristics and understand the infection risk among different populations. The application of network science has the potential to enhance our understanding of and response to the risk challenges posed by emerging infectious diseases.

In order to explore the trust evolution of infrastructures and effectively prevent the online public opinion crisis in extreme climate emergencies. Selecting the “July 20” extreme heavy rainstorm in Zhengzhou, China as the case. Public opinions of Sponge City projects on Sina Weibo were captured. Content analysis, sentiment analysis, and curve fitting method were conducted to identify trust dimensions, users’ behaviors, and evolution patterns. The results indicated that the crisis began with the opinions of integrity-based trust damage from media practitioners, then broke out with opinions of compound-dimensions trust in the guidance of elites and media practitioners. Afterwards, it declined in the authoritative explanation of news organization. In the end, the public opinion crisis subsided with the continuous but low-impact opinions of trust damage by individuals.

The practice of elderly service ecological cannot be separated from the co-creation and integration of multiple subjects. Based on the theory of service ecosystem, we constructed a three-party evolutionary game model of "elderly users-digital support platform-senior care service enterprises" and introduced the government intervention, and deduced and verified the dynamic evolution process and influencing factors of the stabilization strategies of each participating subject. The study shows that the government, as an important regulator of the elderly service ecosystem, can help the overall smart elderly service ecosystem to move towards a stable and win-win situation through the creation of a high-quality business environment, the introduction of digital technology and equipment, the implementation of reasonable rewards and penalties, the reputational evaluation system, and the practice of a dynamic regulatory network.

For constructing a five-dimensional chaotic system with complex chaotic properties and improving the security of image data protection, this paper adopts a cubic nonlinear type magnetronic memristor as the feedback term of the system, combines a four-dimensional chaotic system with the memristor and adds a fixed constant term and a linear feedback controller to obtain a five-dimensional magnetronic memristor chaotic system, and the system generates a coexisting hidden attractor under the influence of a parameter, and it can observe the Limit rings, hidden attractors, weak chaos and other types of attractors are observed. A chaotic image encryption algorithm using chaotic sequence encryption is proposed in combination with the disruption-diffusion algorithm, and the experimental results show that the algorithm has high security.

In response to the issue of credit chaos during credit repair implementation, this study constructs a tripartite stochastic evolutionary game model which involves the government, credit agencies, and the public. Leveraging Itô stochastic differential equation theory, the stability of behavioral strategies for the subjects is analyzed, and combined with numerical simulation to analyze the influence of key variables on the dynamic evolution of game players. The research results reveal that government guidance plays a prominent role in poor social credit environments. In a favorable social credit environment, the government should implement phased and graded regulation to avoid “regulatory capture”. As public recognition and government regulation improve, the effectiveness of governance experiences significant enhancement. Moreover, credit agencies display greater sensitivity to reward parameters than penalty parameters, necessitating the implementation of reasonable incentive and punitive measures by the government. Finally, relevant suggestions are made based on the research findings, which provide effective ideas for the governance of credit chaos and the healthy development of the social credit environment.

In order to enrich the chaotic system model, a four-dimensional hyperchaotic system is constructed based on the Chen chaotic system. By analyzing the dissipation, equilibrium points, stability, sensitivity to initial values, bifurcation diagram, Lyapunov exponent spectra, LE dimension, power spectra and poincaré mapping of the new chaotic system, the rich and complex dynamic characteristics of the new chaotic system are revealed. In order to further enhance the security of information in secure communication, the new chaotic system and Qi hyperchaotic system are synchronized by using the transform modified function projective synchronization method, and a synchronization controller is designed to realize fast synchronization between hyperchaotic systems with different structures. The theoretical analysis and simulation results are consistent. Compared with the adaptive synchronous controller, the time required for the drive system and the response system to achieve synchronization is obviously shortened, which reflects the superiority of the method proposed in this paper.

In this paper, the infinite horizon linear quadratic (LQ) optimal control problem for mean-field system with unknown system information is solved by using a completely model-free reinforcement learning (RL) approach. Although the introduction of the mean-field terms in system dynamics and the cost function will destroy the adaptiveness of the control law, the optimal stabilization control is successfully obtained based on the proposed RL algorithm and the Least Squares Temporal Difference estimation. In addition, combined with the idea of introducing off-policy learning, the control policy is further improved. We also prove that the algorithm produces stable policies given that the estimation errors remain small.

To study the impact of government subsidies on different recycling channels in the new energy vehicle remanufacturing supply chain, a multi-objective model under dual recycling channels is established, an improved robust optimization method is used to solve the problem of uncertainty in demand and recycling volume during recycling, and a convolutional neural network (Conv-GLU network) method is proposed to solve the model. By comparing the performance of online and offline recycling channels, joint recycling channels and recycling channels under government intervention, the multi-objective optimization under government intervention is optimal. Therefore, the government can reasonably intervene in recycling under the background of big data to help new energy vehicle enterprises establish a dual recycling channel remanufacturing green supply chain.

In order to explore the influence of driver visual angle on manual car-following decision-making, a car-following model considering the expected visual angle is proposed based on the visual angle model. Considering the vehicle width, speed and driver risk perception, the expected visual angle function is constructed, and the improved VA model is established by using the expected visual angle as the direct feedback control term. Newton iteration method is used to solve the condition of linear stability of traffic flow. Numerical simulation and parameter calibration verify the improvement effect of the model. The results show that the traffic flow stability of the model in this paper is higher than that of the VA model. Considering the expected visual angle and collision risk perception is beneficial to enhance the stability and safety of traffic flow and improve the fitting accuracy of the model.

To overcome the problem of insufficient feature extraction capabilities of traditional target recognition algorithms in complex scenarios, a new target recognition algorithm based on a hybrid convolutional neural network is proposed. The core of the algorithm lies in combining the learning capability of non-Euclidean domains with traditional convolutional neural networks to enhance the depth and breadth of feature representation. The algorithm in this paper can extract and strengthen the key feature information in target recognition, and significantly improve the accuracy and robustness of recognition.

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.

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 F₁ score indexes of the proposed model have achieved effective improvement.

A voice encryption algorithm based on chaotic sequences and dynamic Joseph rings is proposed. The digitized voice data is used as input to the SHA-256 algorithm to generate a Hash value. The dynamic key and the external input key are combined to generate the initial value of the chaotic system, and the chaotic sequence key stream is generated by the system iteration. The chaotic sequence key stream is used to replace the step size parameter of the Joseph ring. The dynamic Joseph ring with variable step size is used to generate a scrambling matrix. The scrambled data and the chaotic sequence key stream are used for XOR operation to realize the diffusion encryption of voice information. The numerical simulation and security analysis verified the feasibility and security of the voice encryption algorithm.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Magnetronic memristor is introduced into the Morris-Lecar neural system to describe the induced current induced by magnetic flux, and the effect of memristor parameters on the dynamical characteristics of the system is explored. Based on the relationship between charge and magnetic flux, a memristive Morris-Lecar neuron model is established, the discharge patterns of the system are numerically simulated, and the synchronization transition process of the coupled system is researched by using the similarity function, and it is concluded that the strength of the electric coupling and the memristor parameters have a modulating effect on the synchronization state of the system. An asymmetric locally coupled memristive neural network model is constructed, and the effect of coupling strength on the existence of neural network embedded states is researched by using spatio-temporal dynamical diagrams, which further reveals the intrinsic mechanism of the information encoding and transmission process of complex neural network systems.

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.

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.

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.

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.

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.

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.

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.