This paper aims to address the problem that existing network visualization layout algorithms fail to fully consider the characteristics of connected edge symbols in symbolic networks. To this end, we propose a new algorithm to optimize the mechanism of inter-node forces by adjusting the node positions according to the connecting edge symbols by adjusting the node forces and considering the global equilibrium. Experimental results show that the algorithm can visualize the positive or negative relationships in the symbolic network and enhance users' understanding of the network topology. In addition, we propose new network layout aesthetics metrics to quantify the layout quality and effectively reduce the edge length bias and the number of edge crossings. This study provides new methods for visualizing symbolic networks and helps to deeply understand complex network structures.

The spontaneously formed network in the knowledge collaboration of open interaction platforms is extremely complex and large-scale. Therefore, a stochastic process model is proposed to simulate the evolution process of group opinions. The method of network decomposition and spectral clustering algorithm are used to decompose the network into subgroups of different levels. For different types of rule networks, the transition probability matrix and its recurrence formula are given to realize the extension of similar structures. Then, the evolution process of opinions in groups with different structures is simulated while keeping the proportion of opinions unchanged. Finally, an opinion diversity index is proposed to examine the “echo chamber effect”, which considers the influence of adjacent nodes’ opinions. Simulation and empirical results show that the distribution of opinions among adjacent nodes can influence individual preferences, leading to local polarization phenomena, which verifies the effectiveness of the model and index. This model and index help to explain the evolution mechanism of opinions in complex networks, and lay a foundation to improve the quality of knowledge service.

This study focuses on the optimal dismantling problem in multiplex networks under layer node-based attacks. We propose two novel algorithms that integrate intra-layer structural features and inter-layer connections to precisely evaluate node importance, effectively identifying critical nodes essential for network structure and function. Extensive testing on both synthetic and real-world multiplex networks demonstrates that the proposed algorithms efficiently identify key layer nodes, generate smaller dismantling sets, and maintain low time complexity, making them well-suited for large-scale multiplex networks.

Aiming at the problem of detecting dangerous speech leaders in weak relational networks, this paper proposes a method for detecting dangerous speech leaders in weakly connected social networks. The proposed method is based on multi-representation fusion. It determines the sentiment and sensitivity of users' speech to evaluate their professionalism representation. Users' speech is used as nodes to construct a social environment network, and a graph neural network is employed to calculate text co-occurrence relationships and the importance index of users within this network. The user activity representation in social network is then integrated to detect dangerous speech leaders. The results show that the proposed method has better performance compared to baselines.

To more accurately reflect the diverse and characteristics of heterogeneous complex networks, a novel model of two multi-weights complex networks with distinct dimensions and structures is proposed. A new adaptive synchronization controller is designed based on the method of adaptive control and Lyapunov stability theory. Through rigorous theoretical derivation, sufficient conditions for achieving generalized outer synchronization of the two networks are obtained. In contrast to existing literature, the properties of network individual nodes and external coupling matrices can be different. Finally, two numerical simulation examples are presented, and the results demonstrate that the proposed method is a feasible and effective approach for achieving outer synchronization in such networks.

For real networks where the attribute length of connected edges affects the load capacity of edge-dependent networks, this paper proposes a load capacity-weighted model considering the length of connected edges to analyze the cascading failure process of edge-dependent networks in ER-ER, BA-BA, heterogeneous ER-BA networks and power-information-dependent networks. The effects of different load allocation strategies, network structures, different capacity factors and different attacks on the robustness of edge-dependent weighted networks are investigated when the networks fail at the edges. The results show that, the dynamic residual capacity load allocation strategy proposed in this paper can improve the robustness of the network; Increasing the capacity factor in the corresponding range significantly improves the robustness of the network; BA-BA networks are least able to resist large-scale random failures; Compared to typical networks, edge-based deliberate attacks are more destructive in power-information dependent networks.

This paper proposes a new railway-economic multilayer networks with heterogeneous coupling by considering the real-life correlation between the railway transport and economic operating systems to analyze the robustness of the two systems under the impact of disasters. This study analyzes the robustness of this multilayer networks by simulating the impact of disasters on networks as random failure, deliberate sabotage, and local failure. It was determined that the resistance of the railway network is higher than that of the economic network. Furthermore, the critical nodes and edges of the railway and economic network were identified through deliberate sabotage. The distribution of local failure critical node clusters that have the strongest impact on the robustness of the system is different for various radii at local failure.

Focused on the issue that the connection mode and activity of nodes in the identification of important nodes in temporal networks are changed with time, and the complexity of the network structure around nodes is considered. In this paper, a new algorithm called Temporal Penalized Local structure Entropy Advancement (TPLEA) was proposed to identify important nodes. The algorithm was combined with the time window graph model and the Penalty Local Structure Entropy Advancement (PLEA) model, and introduced node activity weight and the contribution rate weight of node degree to determine the comprehensive weight of the node, and finally obtained the importance of each node. The effectiveness and applicability of the method were verified on six real datasets, and ablation experiments were carried out on the introduced weight factors. The experimental results show that this method can effectively identify the important nodes in the temporal network, and the comprehensive weight factors of the nodes have a great influence on the recognition effect of this method.

To improve the real-time performance of trajectory planning for unmanned helicopters with tail rotor jamming, a flight trajectory planning method based on imitation learning is proposed. A nonlinear Model Predictive Control (MPC) trajectory planner is used to solve the optimal landing trajectory and is treated as the expert strategy. This planner is used to collect expert demonstration data in various scenarios to construct an imitation learning database. Subsequently, a deep neural network is built to perform behavior cloning, with data aggregation methods applied to enhance the network's performance, thereby enabling the imitation of the expert strategy. The proposed method can plan reasonable trajectories in various complex simulation scenarios, and the behavior cloning network has a shorter planning time compared to the nonlinear MPC trajectory planner, indicating better real-time performance.

In this paper, the formation control and convergence rate optimization of discrete and continuous time multi-agent systems with a given topology are studied. For the discrete multi-agent formation system, the range of control gain to make the system reach the stable state and the maximum convergence rate are obtained according to the properties of spectral radius. A continuous time multi-agent system formation control method is obtained by applying a set of constant perturbations to the continuous time multi-agent system. Finally, for the two systems mentioned above, an algorithm is given to increase the convergence rate by applying unilateral disturbance to the system.

This paper proposes a novel three-dimensional autonomous chaotic system in order to discover more chaotic behaviors in electrons and circuits, which includes four parameters and three nonlinear coupling terms. Based on the Lagrangian stability theory, the quantitative estimate expression of the ultimate bound of this system was strictly derived by constructing the generalized Lyapunov function. A new sliding mode control strategy was designed based on the Vaidyanathan theorem, achieving global asymptotic synchronization of the system. The research results show that the system has a global exponential attractive set. Numerical simulation verifies the strong robustness and fast convergence of the sliding mode control, and its performance is superior to the adaptive control. This achievement not only enriches the theory of chaotic systems but also provides an effective control method for engineering applications.

In order to explore how two manufacturers producing mutual substitutes make pricing decisions, the evolutionary game models were constructed in three different cases, including the retailer, and the complex dynamic behaviors were analyzed using nonlinear theories. The results show that, when the retailer has service cost input, two manufacturers will increase the wholesale prices, and considering price difference is unfavorable to the one with higher production cost; too fast price adjustment speed will make the system fall into chaos; the increase of cross-price sensitivity coefficient and price ratio coefficient will reduce the wholesale prices of two manufacturers; the delayed feedback and state feedback compound control method was designed to control the unstable system.

For a type of rotating pendulum supported by a spring, it was found that the system has infinite coexisting steady states (attractors), which displays periodic distribution in the phase plane. If at least three connected basins share the same boundary in the phase plane, it is called a complex Wada basin topological boundary. It was found that the basins of the infinitely stable states of the rotating pendulum have Wada basin topological boundaries, and the infinite many basins all have generalized basin cell geometric structure. The complex Wada basin boundary characteristics presented by the rotating pendulum can easily lead to the unpredictability of the final state of the system within the characteristic parameter range and the extremely sensitive dependence of the motion state on the initial conditions. The research results further enrich the dynamics of the rotating pendulum system.

To enhance load forecasting accuracy, a short-term load forecasting model incorporating Beluga Whale Optimization (BWO), Sample Entropy (SE), Variational Mode Decomposition (VMD), and Deep Extreme Learning Machine (DELM) is proposed. Initially, based on the principle of minimizing the local sample entropy of each component, using the BWO optimization algorithm to iteratively optimize the mode decomposition number and penalty factor of VMD, thereby decomposes the power load sequence into high-precision sub-sequences. Subsequently, a DELM load forecasting model is constructed for the decomposed load sequences, with initial weights and thresholds optimized using BWO. Feature selection and extraction are then performed using the Pearson coefficient method on input features. Finally, experimental validation is conducted using real load data from a specific location in Australia. The experimental results demonstrate a reduction of the mean absolute percentage error (MAPE) to 16.9% for the load forecasting model. Comparative analysis against mainstream forecasting models confirms its superior accuracy, validating its effectiveness.

Location selection, inventory and routing decisions are three closely related problems in logistics systems. In order to address the supply disruption caused by uncertain factors, this paper established a mixed integer programming model for location-inventory-delivery integrated optimization problem considering disruption risk, proposed a solution method based on fruit fly optimizer and arithmetic optimizer algorithm, which introduce the exploration and exploitation mechanism of arithmetic optimization algorithm into FOA to increase population diversity. The ability of global optimization and local exploitation of the algorithm is well balanced. The results show that the new algorithm has faster convergence speed and higher convergence accuracy. The results of sensitivity analysis show that the location scheme considering the disruption risk can reduce the expected total cost of the system, and the penalty cost factor has a great influence on the cost and location scheme.

Differing task sequences in a four-way shuttle warehouse system result in varied paths for shuttles and lifts, impacting operation time and energy usage. A collaborative operation model between composite lifts and shuttles is proposed to minimize these metrics, incorporating a dual-objective optimization model that addresses conflicts in task executions on the same level and aisle. An enhanced sparrow search algorithm with heuristic initial population generation, nonlinear decreasing weights, and Gaussian mutations improves optimization. Validated through simulations, the model and algorithm significantly enhance outbound operational efficiency and reduce energy consumption.

In order to improve the micro driving behavior resolution of a traffic cellular automaton(TCA) model, an intelligent driving model(IDM) embedded in TCA was proposed to form a new intelligent car-following traffic cellular automaton(ICTCA) model. Based on the definition of cell-spatial granularity, perturbation experiments were designed to simulate the car-following hysteresis behavior of a platoon leaving the intersection with small disturbances. The results showed that the new model has the ability to resolve the car-following hysteresis, and the finer the cell-spatial granularity, the more stable hysteresis effect can be obtained, indicating that the proposed model has the micro driving behavior resolution close to that of the continuous car-following model under appropriate cell-spatial granularity. Inheriting the characteristics of IDM and TCA, the new model has more possibilities to be applied to intelligent networking scenarios.

In order to obtain the state information of delayed memristive neural networks with reaction-diffusion terms more accurately, this paper designs a H_∞ state estimator. Firstly, based on the Lyapunov-Krasovskii (L-K) functional method, a new delay-product-type augmented L-K functional is constructed to handle the effects of time-varying delays. Then, by utilizing techniques such as free-weight-matrix method, Wirtinger-based integral inequality, and extended reciprocally convex matrix inequality, further reduction in conservatism of the obtained results is achieved. Meanwhile, Dirichlet boundary conditions and Green formula, among others, are employed to address the reaction-diffusion terms of the system; finally, sufficient conditions for the global asymptotic stability of the error system that meet specific H_∞ performance criteria are provided. Building upon this foundation, we present a design methodology for state estimator in terms of linear matrix inequalities. Finally, a numerical example is given to verify the effectiveness of the proposedH_∞state estimator.

Early warning signals (EWS) from the theory of critical slowing down can anticipate the threshold of disease elimination process and provide scientific guidance for disease elimination plans. In this paper, we consider the SIR stochastic model with multiple simulations for incidence data and calculate the area under the curve to evaluate the effect of EWS behaviors. We find that EWS remains effective even at high initial levels of immunity, although its effectiveness diminishes compared to scenarios where the initial immunity rate is zero. Mean and variance are sensitive to the system with a decrease in the number of cases, while the coefficient of variation is not only robust but also exhibits excellent discriminatory effects as the system approaches or moves away from the tipping point. Autocovariance, lag-1 autocorrelation and decay time increase before the system approach to the tipping point.