Through designing effective delayed feedback and open-loop controllers, the cluster lag synchronization problem of fractional order community network is studied. For different communities of the network, both the node dynamics and the lags with synchronization goals are nonidentical. Based on the Lyapunov function method and the stability theory of fractional order system, the sufficient condition for achieving the cluster lag synchronization is derived. Finally, the correctness and effectiveness of the theoretical results are verified by numerical and simulation examples.

To find theoretically an effective antitrust policy, we design an access rule for nodes based on the rearrangement of their fitness and study its effect on the topology condensation from the perspective of complex network theory. By Monte-Carlo simulations and the finite size scaling analysis, we obtain the critical rearrangement index for a typical class of fitness distribution and establish the condensation phase diagram. The phase diagram shows that there exists an interval of the critical rearrangement index, outside which the condensation will be effectively suppressed; the phase diagram is asymmetric in structure and the critical reverse-rearrangement index diverges in a nonlinear manner. These results can explain the present monopolistic behavior by internet firms and provide useful suggestion for the corresponding anti-monopoly policy.

Based on the good application prospects of multi-agent systems, we study the graph-theoretic conditions of target controllability for a class of special general linear multi-agent systems under undirected weighted topology. By using the knowledge of graph and matrix theory, a sufficient condition for the target controllability of the system is obtained. Then, through the analyses on actual examples, we obtain a necessary and sufficient condition of target controllability for the system. The results show that under the leader-follower connected topology, the multi-agent system is target controllable if and only if the connected component containing the follower target nodes is target controllable, and the same conclusion applies to the non leader-follower connected topology.

To scientifically evaluate the resilience of China′s industrial chain and promote high-quality economic development, this paper employs complex network theory and utilizes data from China′s multi-regional input-output table to construct a simulated attack model of the industrial chain network, thereby measuring the resilience of the industrial chain. The results show that the industrial chain layout of 31 provinces in China exhibits obvious local correlation attributes, and presents a collaborative development characteristic led by key regions and industries; The overall resilience of China′s industrial chain is strong, and during the inspection period, the overall resilience index of China′s industrial chain shows an upward trend; There is a significant gap in the resilience of the industrial chain between regions and industries in China.

Aiming at the problem of nodes-set mining in express logistics network, this paper constructs DW-KPP-Pos (Directed Weighted-Key Players Problem-Positive) model based on KPP-Pos (Key Player Problem-Positive) and designs a heuristic algorithm to improve the efficiency of the model. The empirical analysis of China’s urban express logistics network shows that: The DW-KPP-Pos model with heuristic algorithm can efficiently mine “Maximum spread seeds group” in express logistics network. Including Shanghai, Chongqing, Guangzhou, Beijing, Jinhua and Hong Kong; The comparison of measurement results suggest that the propagation efficiency of nodes-set K mined by DW-KPP-Pos model is 0.59%, 0.88% and 6.19% higher than that of degree nodes-set K_deg, PageRank nodes-set K_pag and betweenness centrality nodes-set K_bet respectively. In this paper, a new method of nodes-set mining considering maximum spread effect is proposed, which can provide technical support for the layout of express logistics infrastructure.

The SEIQRDP propagation model has seven types of states: susceptible state, non susceptible state, exposed state, confirmed state, isolated state, cured state, and dead state. By introducing isolation control strategies, it was constructed a SEIQRDP_G transmission model, the number of susceptible populations that infected individuals come into contact with will decrease per unit time, protecting the population of susceptible individuals,which can better than a comprehensive open strategy. By introducing vaccine control strategies, four different modified SEIQRDP transmission models were constructed to improve the immune capacity of susceptible populations and reduce mortality rates. The model use the basic reproduction number, and the decision coefficient and median absolute error as evaluation indicators, the real epidemic data of the model in Changchun City were empirically analyzed. The experimental results indicate that the SEIQRDP_G transmission model is most suitable for practical epidemic data; the SEIQRDP_ Y_ 1 and the SEIQRDP_ Y2_ 2 propagation model have the lowest basic regeneration number; the determination coefficients of the SEIQRDP_Y2_1 and SEIQRDP propagation models are the least. Through the introduction of control strategies, the transmission mechanism of the epidemic was further characterized.

In order to reveal the generation mechanism of chaos, the mechanical mechanism of forced Lorenz model is discussed. The forced Lorenz model is transformed into Kolmogorov system, and the torques of the system are decomposed into inertial torques, dissipative torques and external torques. The effects of various torque coupling modes on the System dynamics behavior are analyzed to reveal the mechanism of chaos generation. It is shown that only when the dissipation factor, the driving factor and the internal energy exist in the full moment mode, and the driving factor and the dissipation factor match, the forced Lorenz system can produce chaos. The global stability of the forced Lorenz model is analyzed by constructing the Casimir function, and the boundary of the attractor of the forced Lorenz model is estimated.

To explore the question of whether there exist common Wada basin boundaries among an infinite number of coexisting attractors, we extended Nusse-Yorke′s theorem for finite Wada basins to the scenario of infinite Wada basins. Through numerical experiments conducted on a class of nonlinear oscillators, we discovered that within this class, there are infinite coexisting attractors that share common basin boundaries, and these attractors exhibit periodic spatial distributions. Further analysis of the intricate Wada basin structures associated with these attractors, employing a generalized version of Nusse-Yorke′s theorem concerning Wada basins, confirmed the presence of common boundaries among these interconnected Wada basins. Finally, it is essential to note that this type of Wada basin boundary exhibits highly complex nonlinear dynamical characteristics, potentially leading to significant uncertainty and extreme sensitivity to initial conditions.

The existence and metric characteristics of a class of quasiperiodic ally driven two-dimensional systems with sinusoidal functions are studied. Firstly, the birth process of strange nonchaotic attractors is described by phase diagram. Strange nonchaotic attractors are fractal due to the interruption of smooth torus doubling for the fixed parameters. Secondly, the strange nonchaotic attractors is confirmed by the largest Lyapunov exponents and phase sensitivity exponents. Finally, the power spectrum, finite Lyapunov exponents distribution and recurrence plots are used to characterize the strange nonchaotic attractors. According to the experimental results, there are strange nonchaotic attractors in the system and have good statistical characteristics.

Aiming at the state tracking problem of multi-agent systems, this paper studies the event triggered collaborative control of high-order nonlinear multi-agent systems with input dead zones. First, the dead zone model is transformed into linear terms and perturbed terms. Then, using the fuzzy logic system to model the follower to reduce the influence on the system performance. Finally, designing the event triggering control to save bandwidth and further reduce the communication burden of the system. In addition, the proposed method can not only ensure the consistency of the leader and the followers, but also has been proved that the proposed control scheme is not affected by Zeno phenomenon. The simulation results are used to verify that all states of the follower of the design scheme are synchronized with the state of the leader.

A fast finite time containment control strategy is designed for multi-manipulator systems in random vibration environment. The addition of finite-time filter avoids the problem of ‘computation explosion’ when differentiating the virtual control signals by traditional backstepping and improves the convergence speed of the systems by finite-time. By establishing the error compensation mechanism, the influence of filter errors to the control systems is eliminated. Using the relative threshold-event-triggered mechanism effectively reduces resource waste and communication burden. It proves that closed-loop systems are actually fast and finite time stable in mean square. The MATLAB simulation results show the effectiveness of the control strategy.

To explore the impacts of dividend volatility on the evolution characteristics of stock prices, this paper constructs a heterogeneous investor model, and analyzes this model through theoretical derivation, numerical simulation and empirical testing. The main research conclusions include: The state of stock price evolution is sensitive to the learning intensity of the trend investors. When the learning intensity is low, the stock price would converge to its basic value. When a certain threshold is exceeded, the stock price deviates from its basic value and shows a new equilibrium. With the further increase of learning intensity, the stock price will show a closed-loop cyclic solution. There is also a threshold for the dividend volatility. The impacts of dividend volatility on the volatility of stock price are in the opposite direction on two sides of this threshold.

To investigate the impact of carbon emission cost sharing on supply chain decisions, four carbon emission cost sharing supply chain decision models for manufacturers and retailers are developed. The Stackelberg game is applied to solve the problem, and the four decision-making models are analyzed based on evolutionary game theory, and the equilibrium conditions of the evolutionary stable strategy of carbon emission reduction cost sharing are obtained. Research shows that manufacturers′ profits are directly proportional to the proportion of low-carbon investment cost sharing, and are first proportional and then inversely proportional to the proportion of low-carbon marketing cost sharing; Retailers’ profits decrease with the increase of low-carbon investment costs and marketing cost sharing ratio. When the proportion of low-carbon investment and marketing cost sharing, the coefficient of low-carbon investment and marketing cost, and the sensitivity coefficient of consumers to marketing efforts and carbon emissions reduction are within a certain range, the system will reach a stable strategy. Finally, based on the research findings, relevant suggestions are proposed, providing effective ideas for the sustainable development of low-carbon cost sharing businesses in the supply chain.

In order to ensure that urban emergency supplies can be delivered to the demand point in a timely and accurate manner, especially for special emergency supplies with a short life cycle′ perishable goods, its timeliness requirements are higher. Based on the emergency scenario of sudden public health events, this paper establishes a multi-objective location model of urban perishable goods distribution center with the goal of minimizing transportation time and transportation cost and maximizing relative coverage area. The Harris Hawk optimization algorithm (HHO) is improved to achieve an effective solution to the multi-objective location problem of perishable goods distribution center. In order to verify the effectiveness of the model, a district in Shanghai is selected as a research example. The results show that the improved HHO algorithm can solve the location model of perishable goods distribution center under actual urban road conditions, and can provide an intuitive multi-objective location optimization scheme.

In order to explore the evolution mechanism of each participant’s behavior strategy selection on network platform employment governance, a tripartite evolution game model of "platform enterprise-laborer-government" is proposed based on evolution theory. This paper analyzes the main influence factors of each participant’s behavior strategy selection which include their own profits, government punishment and social reputation. And some suggestions on network platform employment governance are put forward. The effective way of network platform employment cooperative governance can be concluded as building platform enterprise self-regulation system, laborer employment ecosystem system and government service system under the new forms of employment.

For the two-player game problem, on the basis of Q-learning algorithm, the state-value function is updated by using neural network parameter approximation, the adaptive gradient optimization algorithm is selected for parameter updating, and the behaviors of the two agents are regulated by the Nash equilibrium idea. At the same time, in order to improve the protection effect of the model, differential privacy protection is added to the results to ensure the security of the data in the process of the two-player games. Finally, the experimental results verify the usability of the algorithm, which is able to train two agents to reach their respective target points stably after multiple rounds.

To address issues such as poor matching, low trust between principal agents, and jump-dealing in task outsourcing, quantum game methods are used to expand the participant strategy space through a quantization process. The task matching "entanglement" is described in the form of closeness degree by processing the cumulative distribution function, and a pareto equilibrium solution for each participant is achieved at the lowest energy level state.

Aiming at the problems of high collision rate and low traffic efficiency caused by conflict risk of intelligent vehicles in single intersection environment, a path planning algorithm based on local game algorithm is proposed. By establishing the intersection conflict risk model, the conflict risk is analyzed, and the conflict resolution method between vehicles and pedestrians is proposed. The local game theory is introduced to establish the profit function to evaluate the feasible decision, and the solution of the pure strategy Nash equilibrium under the constraint condition is obtained. The vehicle speed is planned, and the path planning of the intelligent vehicle is finally realized. The simulation results show that the proposed path planning algorithm improves the interaction success rate by 9.32% compared with the evolutionary game and cooperative game algorithm under different traffic flows, and the traffic efficiency increases by 33% on average, which can effectively alleviate the traffic pressure.

The study of congestion evolution mechanism in terminal airspace is a vital measure to ensure the normal operation of terminal airspace. This paper divides congestion into two categories: its own structural causes and external causes, and establishes a corresponding analytical model for congestion formation and dissipation. Based on the characteristic indexes of traffic flow evolution and Greenshields theory, the cusp catastrophe analysis model for congestion mechanism is established. In order to verify the validity of the model, this study takes the Chengdu terminal airspace as the object and uses AirTOp software to generate simulation operation data. The results show that the designed model can effectively describe the macroscopic process of congestion evolution, and the mechanism of congestion evolution can be effectively analyzed through the changes of equivalent flow, density and wave speed in the segment.

In order to clarify the risk factors of food safety issues in the traditional catering business and find effective measures to address issues from the source. The fault tree is constructed to identify risk factors, and qualitative analysis of risk factors is done by using the minimum cut set and structural importance. Moreover, the fault tree model is transformed into a Bayesian network, and final BN model is finished by structure learning and parameter learning based on case data. The two-way reasoning ability of BN is used to conduct quantitative analysis, and sensitive factors of various types of problems from the perspective of catering operators are finally obtained. The results indicate that personnel management is most likely to cause problems. Insufficient training is an important reason for food safety issues.

This study proposes a new method to improve short-term load forecasting accuracy. The method is based on Variational Modal Decomposition (VMD) with consideration of VMD residuals and an Improved Northern Eagle Algorithm (INGO) optimized Bi-directional Long Short Term Memory (BiLSTM) network. The VMD is used to decompose historical load data into multiple eigenmode components (IMFs) and a residual quantity. The BiLSTM model is then constructed separately for each IMF and residual, as well as the associated meteorological parameters. To avoid the impact of poorly selected hyperparameters on prediction accuracy, the INGO algorithm optimizes the implied layer nodes, training times, and learning rates of the BiLSTM. Last but not least, the prediction results are superimposed to obtain the final results. By analyzing specific cases, this paper′s method has demonstrated a higher prediction precision when compared to alternative methods. This validation confirms the effectiveness of the method presented in this article.