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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.