This paper investigates opinion intervention of the heterogeneous Deffuant-Weisbuch (DW) model in social networks, whose bounded confidence and the random encounter communication mechanism make the evolutionary outcomes almost unpredictable. We employ a goal-oriented leader and a coordinating leader to guide the divisive and unpredictable public opinions to a desired state. The goal-oriented leader maintains the desired state, while the coordinating leader, with a large confidence threshold, guides agents towards the goal-oriented leader. Both leaders follow the same DW model update rules as normal agents and do not alter normal agents' opinion update rules or require their private information, thus ensuring a gentle intervention process. We theoretically derive a necessary and sufficient condition on the parameters of the leaders for them to guide all agents' opinions to reach consensus at the desired state almost surely, regardless of the parameters of normal agents. Furthermore, we prove that both types of leaders are necessary for successful intervention, whereas one leader alone is insufficient. (c) 2025 Published by Elsevier Ltd.

BACKGROUND:Estimating the instantaneous reproduction numbers (Rt) requires inferring generation time (Rt>, the interval between successive infections in the transmission chain), often approximated by the serial interval (SI, the interval between successive onsets in the transmission chain). The serial interval based on clinical outcomes is subject to recall biases, and such clinical information is not always available. As a comparable metric, we defined the diagnostic serial interval (SId, the time between diagnostic reporting of case pairs in a transmission chain) and compared it with the traditional SI. METHODS:We analyzed confirmed COVID-19 cases from three ancestral waves in Hong Kong and the first wave in mainland China. Using Bayesian methods, we inferred the distributions of effective SI and SId, along with onset-to-reporting delays, and compared the resulting Rt estimates. RESULTS:The distributions of SI and SId were comparable across waves, with shorter means observed in SId. Reporting delays for infectors were longer than those for infectees, which was identified as a key factor influencing the temporal variation in SI and SId. Additionally, factors such as public health and social measures (PHSMs), case profile, and demographics were found to significantly impact the estimates. Time-varying estimates of the reproduction number derived from both SI and SId were highly consistent, with median absolute differences ranging from 0.12 to 0.19. CONCLUSIONS:The diagnostic serial interval shows potentials as a comparable metric to the traditional serial interval for estimating transmissibility in assessing COVID-19 transmission dynamics, and this approach could be extended for other respiratory viruses.

With the rapid development of connected and automated vehicles (CAVs) and intelligent transportation infrastructure, CAVs and connected human-driven vehicles (CHVs) will coexist on the roads in the future for a long time. This paper comprehensively considers the different traffic characteristics of CHVs and CAVs, and systemically investigates the unsignalized intersection management strategy from upper decision-making level to lower execution level. Combined with the designed vehicle planning and control algorithm, the unsignalized intersection management strategy consists of two parts: the heuristic priority queues based right of way allocation (HPQ) algorithm, and the vehicle planning and control algorithm. In the HPQ algorithm, a vehicle priority management model considering the difference between CAVs and CHVs is built to design the right of way management for CAVs and CHVs, respectively. In the lower level for vehicle planning and control algorithm, different control modes of CAVs are designed according to the upper level decision made by the HPQ algorithm. Moreover, the vehicle control execution is realized by the model predictive controller combined with the geographical environment constraints and the unsignalized intersection management strategy. The proposed strategy is evaluated by simulations, which show that the proposed intersection management strategy can effectively reduce travel time and improve traffic efficiency. The intersection management strategy captures the real-world balance between efficiency and safety for potential future intelligent traffic systems.

Incentive-based control mechanisms in game-theoretic models aim to steer players toward socially desirable strategies through appropriately designed utility rewards or penalties. In this paper, we propose an algebraic framework for incentive-based control in networked evolutionary coordination games (NECGs) under asynchronous myopic best-response dynamics. We establish a fundamental connection between the reward policy and the attainability of a desired equilibrium, demonstrating that a fully cooperative equilibrium is implementable if and only if there exists a reward vector that makes it reachable from the initial fully non-cooperative strategies in the incentivized NECG. Moreover, leveraging the strategy profile reachability sets, we demonstrate that the incentive control problem reduces to verifying the reachability of the set associated with the desired equilibrium. We prove that the reachable set of the desired equilibrium in the original NECG is contained within that of its incentivized counterpart. This, to some extent, simplifies the verification for computing the reachable set of the desired equilibrium in the incentivized NECG. Finally, we show an example to illustrate the proposed result.

This article addresses vision-based aerial target tracking for micro quadrotors operating in unknown and complex environments, where partial observability, frequent occlusions, and aggressive target maneuvers often lead to target loss. The key challenge is to maintain consistent target visibility under the coupled constraints of underactuated quadrotor dynamics and body-fixed camera perception. To address this challenge, we propose a visibility-aware tracking framework that unifies target state estimation, viewpoint planning, and trajectory optimization. An occlusion-aware particle filter with multimodel dynamics estimates the target state under intermittent measurements and performs short-horizon probabilistic prediction, producing time-indexed risk envelopes that capture motion uncertainty. Based on these envelopes, a segmentwise visibility-aware path planner explicitly reasons about visibility to select informative viewpoints using a visibility cost. A spatial–temporal optimization framework incorporates perception-consistent penalties for vertical visibility, lateral occlusion avoidance, and uncertainty-aware longitudinal distance regulation, yielding smooth and dynamically feasible trajectories. Simulation and real-world experiments demonstrate that the proposed system maintains continuous target visibility and reliable tracking in complex environments.

With the development of e-commerce and intelligent manufacturing, the demand for warehouse automation continues to rise, and collaborative multi-robot handling and picking have become key to improving logistics efficiency. However, with limited picking station resources, increases in robot numbers and order complexity easily lead to congestion and deadlocks near picking stations, affecting system stability and efficiency. To address this problem, this paper proposes a multi-robot scheduling and deadlock prevention method based on a loop path movement mechanism. By establishing a circular buffer zone between picking stations and storage areas, robots are guided to move continuously, thereby reducing queuing and the risk of deadlocks. A finite state machine (FSM) model is introduced to dynamically characterize the operational process, and a loop-path scheduling algorithm is designed to optimize system coordination. Simulation results show that the proposed method can completely avoid deadlocks, and compared with traditional buffer area strategy, shortens the order fulfillment makespan by 68 s and increases average utilization by 11.77

During epidemics, behavioral and psychological convergence within societies significantly influences the formation of herd immunity. To investigate the interaction between individual vaccination strategies and disease transmission, this study constructs a two-layer dynamic hypernetwork model coupling disease spread with vaccination behavior: the upper layer represents strategy update, while the lower layer governs disease transmission dynamics. First, disease transmission is simulated using a mean-field compartmental model incorporating nonlinear infection rates and interaction coupling terms. Second, evolutionary game theory is applied to analyze vaccination strategy evolution. Findings reveal that conformity suppresses herd immunity formation; excessive conformity not only weakens collective cooperation but also increases average societal costs. Experiments further confirm: disease transmission is influenced by upper-layer decisions, while cooperation levels in the strategy layer are regulated by lower-layer transmission parameters. Vaccination rates do not monotonically increase with decreasing costs but are affected by multiple interacting factors. Simultaneously, the model reveals that group behavior does not universally drive individual vaccination; instead, it may lead to a persistent increase in susceptible individuals, thereby amplifying the risk of epidemic outbreaks. These findings hold significant practical implications for safeguarding public health and formulating vaccine policies.

This paper studies a system security problem in the context of observability based on a two-person noncooperative infinitely repeated game. Both the attacker and the defender have means to modify the dimension of the unobservable subspace, which is set as the value function. Utilizing tools from geometric control, the authors construct the best response sets considering one-step and two-step optimality respectively to maximize or minimize the value function. The authors establish a unified necessary and sufficient condition for Nash equilibrium that holds for both one-step and two-step optimizations. The proposed analysis further uncovers two evolutionary patterns, lock and loop modes, and shows an asymmetry between defense and attack. The defender can lock the game into equilibrium, whereas the attacker can disrupt the equilibrium by sacrificing short-term utility for longer-term advantage. Six representative numerical examples corroborate the theoretical results and highlight the complexity of possible game patterns.

Ensuring the continued operation of a networked system under various structural disruptions relies heavily on the effective robustness of the system, desirably with optimization. To make this process more efficient, assessing the robustness enhancement potential (REP) in advance helps conserve resources and reduce design and operational costs. This paper proposes a distance to regularity (D2R) structural metric that measures the distance between a network's degree sequence and its closest regular variant so as to capture REP. Two variants, based on Euclidean distance and Kullback-Leibler divergence, are implemented; both exhibit strong correlations with robustness enhancement under connectedness and controllability measures. Experimental results verify that D2R can effectively capture structural heterogeneity relevant to REP and enhance the performances of machine learning models in predicting REP. Compared to deep neural network approaches, D2R-based models achieve lower prediction errors while offering improved computational efficiency. Feature selection analysis further confirms the consistent improvements of D2R over other benchmarks. These findings establish D2R as a reliable lightweight descriptor for robustness-aware network analysis.

Networked systems-from smart grids and autonomous fleets to social networks-are ubiquitous yet complex, with agents interacting amid topological dependencies and challenges like dynamic environments or malicious attacks. Game theory, control theory, and optimization offer tools to model these systems, but bridging theory with real-world complexity remains a key gap. This Chaos Focus Issue tackles this by exploring intelligent game theory in networked systems, featuring 26 papers across four themes: cooperation promotion, distributed systems, complex structures, and game applications. It links theoretical insights (e.g., cooperative dynamics in structured populations) to practical solutions (e.g., epidemic control, infrastructure protection), advancing resilient, efficient networked system design.

High-throughput neutralisation tests could lead to a better understanding of the evolution of human influenza.

We consider the persistence for invariant graphs of twist maps that exhibit the strongest possible dynamics, namely those real-analytically conjugate to rigid rotations, under Gevrey-γ (γ∈ [0,1]) perturbations. By enhancing the regularity of the perturbation itself, we show that invariant graphs with the strongest dynamics can persist even when the size of the perturbation and the constraints on the frequency go beyond the requirements of classical KAM theory and the theory of normally hyperbolic invariant manifolds. The proofs of these results are based on a parameterized direct KAM method.

Cooperation is a fundamental organizing principle in biological and social systems. However, under resource constraints, cooperative behavior often collapses as defectors always gain resources unilaterally in interactions. To address this, we propose a Forced Loner Mechanism (FLM) integrated into the Spatial Prisoner's Dilemma with resource dynamics (SPDL), where bankrupt agents are forced to withdraw and receive a guaranteed subsidy. This mechanism models realistic social subsidies or industrial safety nets. Simulation results indicate that the forced loner mechanism restores cooperation under high temptation to defect. This mechanism significantly improves the overall performance of the game system by enhancing efficiency, sustainability, and fairness. These properties are quantified by three macroscopic indicators: net output, average cumulative resources, and the Gini coefficient, respectively. Moreover, a sensitivity analysis reveals that the mechanism is robust against variations in the Loner payoff. These findings provide a quantitative understanding of how social exit and protection mechanisms can be interventions to stabilize cooperation in resource-limited systems.

The outbreak of COVID-19 in 2019 has made people pay more attention to infectious diseases. In order to reduce the risk of infection and prevent the spread of infectious diseases, it is crucial to strengthen individual immunization measures and to restrain the diffusion of negative information relevant to vaccines at the opportune moment. This study develops a three-layer coupling model within the framework of hypernetwork evolution, examining the interplay among negative information, immune behavior, and epidemic propagation. Firstly, the dynamic topology evolution process of hypernetwork includes node joining, aging out, hyperedge adding and reconnecting. The three-layer communication model accounts for the multifaceted influences exerted by official media channels, subjective psychological acceptance capabilities, self-identification abilities, and physical fitness levels. Each level of the decision-making process is described using the Heaviside step function. Secondly, the dynamics equations of each state and the prevalence threshold are derived using the microscopic Markov chain approach (MMCA). The results show that the epidemic threshold is affected by three transmission processes. Finally, through the simulation testing, it is possible to enhance the intensity of official clarification, improve individual self-identification ability and physical fitness, and thereby promote the overall physical enhancement of society. This, in turn, is beneficial in controlling false information, heightening vaccination coverage, and controlling the epidemic.

The complexities of real-world driving environments, coupled with a limited availability of naturalistic and critical test scenarios, have long hindered unbiased and effective comprehensive performance evaluations. In this work, we propose a bi-level adaptive deep reinforcement learning (BADRL) framework designed to generate realistic and diverse critical boundary scenarios. The method involves training AI-driven background agents to impartially assess the overall performance of autonomous vehicles. By leveraging naturalistic driving data, these agents acquire realistic driving behaviors via a neural model that encapsulates naturalistic driving patterns. To enrich the authenticity and diversity of the test scenarios, a wide array of traffic participants, encompassing vehicles, pedestrians, and bicycles, are meticulously modeled and portrayed to engage in intricate interactive behaviors with the tested autonomous vehicles. To address the challenges of high-dimensional environments, we introduce a scenario complexity model that assesses relative complexity in real time. This model enables the upper-level neural network in BADRL to dynamically escalate scenario complexity, with the resulting scenarios subsequently processed by lower-level models to optimize the actions of primary traffic participants. The BADRL method enables online real-time generation of naturalistic and critical boundary scenarios. Extensive simulation experiments validate the effectiveness of the BADRL approach in diverse driving environments, with results indicating an improvement in the efficiency of critical boundary scenario generation by approximately 15.89 % compared to state-of-the-art methods.

Resource competition and intentional disruptions, grounded in rational intergroup conflict theory, play a central role in driving strategic rivalry in networked games. These mechanisms mirror real-world conflict dynamics, profoundly shaping decision-making processes and interfering with systemic stability. This study investigates the modeling and dynamics of networked evolutionary games with intergroup conflict (NEGs-IC). In the proposed framework, players are assigned a finite number of health points, which decrease when attacked-affecting both survivability and strategic interactions. Leveraging logical dynamical system modeling, we capture the co-evolution of strategies, payoffs, health points, and player actions, demonstrating that NEGs-IC can be effectively represented as a logical dynamic system. To characterize collective interest in NEGs-IC, we introduce an objective function that balances group cooperation and health point attrition. Based on this formulation, we define three evaluation criteria-optimal, suboptimal, and weak-to assess collective interest. An illustrative example is also presented to analyze network-based conflicts, offering insights into strategic behavior in adversarial environments.

The paper introduces an analytical framework for decomposing finite strategic games within the multi-potential game (MPG) paradigm. Specifically, it partitions the finite non-cooperative game space into multi-potential subspace and multi-harmonic subspace, uncovering the common interests and conflicts of player subsets. Additionally, this approach provides a systematic methodology for calculating potential functions within MPGs. Within the MPG framework, a finite non-cooperative game characterized by its minimal potential index qG can be considered as a qG-person non-cooperative game. Furthermore, the Nash equilibrium of this qG-person non-cooperative game is examined. This analysis substantially enhances our comprehension of Nash equilibrium in finite non-cooperative games in terms of group welfare. Finally, an illustrative example is presented to demonstrate the theoretical results.

This article investigates the controllability of networked sampled-data systems with various time delays on both control and transmission channels. Necessary and sufficient controllability conditions are first derived for systems with a single delay and then extended to systems with multiple delays. It is found that delays in control signals have no effects on the overall controllability. For a networked system whose topology matrix has only zero eigenvalues, delays of neither control nor transmission signals will affect the overall controllability. It is proved that an uncontrollable mode 1 of such a networked sampled-data system cannot be altered by arbitrary delays. Finally, the networked sampled-data system with first-order holders is discussed, which is modeled as a variant of time-delayed system, and some easy-to-verify algebraic conditions on the controllability are given based on matrix rank checking.

In Boolean networks (BNs), robustness typically refers to the system's ability to tolerate perturbations in either the state or the rule-based structure, both of which can significantly affect network dynamics. For function perturbation of rule-based structure, most existing studies have focused on analyzing the characteristics of the perturbations or investigating the resulting dynamics through simulations. However, few works have employed external analytical tools, such as Lyapunov-based methods, to evaluate the stability of the perturbed BNs. This paper introduces a Lyapunov-based framework for analysing the robust stability of BNs under one-bit function perturbations. We establish a theoretical result showing that if a perturbed BN admits an adaptively adjustable Lyapunov function to some extent, then it is guaranteed to achieve global finite-time stability at the original equilibrium state. Finally, a numerical example is provided to illustrate the theoretical results. Copyright (c) 2025 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)