Complex strategic interactions of rational agents are ubiquitous in decision-making groups which greatly influence the evolutionary dynamics of many real-life networked systems. Here, we study how individual decision-making behaviors evolve when the topology of network interactions is weighted, and how the network of mixed coordinating and anti-coordinating games is driven to an equilibrium. We prove that the weighted pure coordinating or anti-coordinating decision-making dynamics, under both asynchronous and partially synchronous updates, will converge to the Nash equilibrium after finite strategy switches. Moreover, it follows that the upper bound on the number of switches for the convergence depends on the number of agents and the weights' distribution under asynchronous update. For mixed coordinating and anti-coordinating games, we find that network game dynamics can be decoupled into convergence and nonconvergence regions under certain conditions, in which the global convergence can be established by adding leaf vertices. For more general cases, we devise the incentive mechanisms for agents to achieve the convergence. We also extend the incentive performance of fully asynchronous updating to the partially synchronous updating. Our results provide hints on the typology and incentive mechanisms to induce the convergence of mixed gaming networks.

State estimation is an important property in the operation of logical dynamic systems, and how to analyze and synthesize this property when the estimation conditions are not satisfied is the focus of the current research. This work addresses the synthesis problem of detectability with probability 1 for probabilistic Boolean networks (PBNs) via flip control and optimal-flip-based segmented reinforcement learning (OFSRL). First, in the framework of the semitensor product (STP), the PBN is transformed into an algebraic form to serve as the structure matrix for OFSRL. Depending on the attractor condition in the state pair, the analysis of detectability synthesis is divided into four different cases, and in each case, flip control is applied to the structure matrix and output matrix as actions in the OFSRL framework. Second, the detectability synthesis problem of the PBN is transformed into a set stabilization problem, and to reduce computational complexity, necessary and sufficient conditions based on the reachable set are introduced as criteria for implementing OFSRL. Furthermore, based on the above structure matrix, actions, and criteria, OFSRL is proposed to address the detectability synthesis problem of PBNs and obtain the optimal flipping sequence. Finally, two numerical simulations are conducted to verify the reliability of the proposed conclusions, and comparisons are made between OFSRL, traditional theoretical methods, and conventional reinforcement learning (RL) algorithms to highlight the advantages of OFSRL.

Collective cooperation is fundamental to individual survival and social development, and exploring its mechanism of emergence is of great significance. However, most existing studies related to the evolutionary dynamics on higher order networks assume that all agents within a population follow the same strategy updating rule. This assumption does not align with reality and is an oversimplification. To this end, we propose a higher order network game framework featuring a hybrid strategy updating rule. Specifically, we use scale-free random hypergraphs (SRHs) to characterize the underlying network topology of the population. Then, we categorize agents into two types: imitation learners and autonomous learners according to social learning and behaviorism theories. For imitation learners, we apply the Fermi rule to characterize their probabilistic imitation behaviors, while for autonomous learners, we adopt the reinforcement learning method to highlight their decision-making features. Through a series of simulation experiments and theoretical analyses, we find that autonomous learners have a dual impact on cooperation in groups: they inhibit cooperation at low dilemma intensities but promote cooperation at high dilemma intensities. In addition, we show that smaller group sizes are more conducive to cooperation. Our findings provide valuable insights for better understanding the impact of hybrid updating mechanisms on the evolutionary dynamics of collective cooperation in higher order networks.

Simplicial complexes successfully resolve the limitation of social networks to describe the spread of infectious diseases in group interactions. However, the effects of quarantines in the context of group interactions remain largely unaddressed. In this article, we therefore propose a susceptible-infectious-quarantine- recovered-susceptible (SIQRS) model with quarantines and study its evolution on simplicial complexes. In the model, a fraction of infected individuals is subject to quarantine, but individuals leaving quarantine may still be contagious. Using mean-field (MF) methods, we derive the propagation threshold and the steady state infection densities as well as conditions for their stability. Numerical simulations moreover show that longer quarantine times and higher quarantine ratios tend to disrupt discontinuous phase transition and bistable phenomena that are commonly due to group interactions. Additionally, when epidemic outbreaks are recurrent, although quarantine measures can reduce the peak of the first wave and delay the onset of future waves, they may also lead to an increase in subsequent peak infected densities. This highlights the need to prepare sufficient resources to deal with periodic infections after the initial wave is over.

Overlapping graph clustering is essential to understand the nature and behavior of real complex systems including human interactions, technical systems and transportation network. However, in addition of topological structure, many real-world networked systems contain spare factors, i.e., attributes of networks. Despite the considerable efforts that have been made in graph clustering, they only concentrate on the topological structure, which lack a profound understanding of cluster configuration on attributed graphs. To address this great challenge, in this article, we propose a new overlapping graph clustering algorithm by integrating the topological and attributive information into a cluster potential game (CPG). Firstly, a generalized definition of the utility function is provided, which measures the payoff of each node based on different node-to-cluster distance functions. It is worth mentioning that the model we proposed is able to associate with the classic ordinal potential game well. Then, we define the measures of both tightness and the homogeneity in each cluster, and introduce a novel two-way selection mechanism. The goal is to extend the flexibility of the cluster potential game, so that one can achieve a win-win situation between nodes and clusters. Finally, a distributed and heterogeneous multiagent system (DHMAS) is carefully designed based on a fast self-learning algorithm (SLA) for attributed overlapping graph clustering. Two series of experiments are implemented in multi-types datasets and the results verify the effectiveness and the scalability after the comparison with the most advanced approaches of literature.

Epidemiological models based on traditional networks have made important contributions to the analysis and control of malware, disease, and rumor propagation. However, higher-order networks are becoming a more effective means for modeling epidemic spread and characterizing the topology of group interactions. In this article, we propose a composite effective degree Markov chain approach (CEDMA) to describe the discrete-time epidemic dynamics on higher-order networks. In this approach, nodes are classified according to the number of neighbors and hyperedges in different states to characterize the topology of higher-order networks. By comparing with the microscopic Markov chain approach, CEDMA can better match the numerical simulations based on Monte Carlo and accurately capture discontinuous phase transitions and bistability phenomena caused by higher-order interactions. In particular, the theoretical solution to CEDMA can well predict the critical point at continuous phase transition and corroborate the existence of the discontinuous phase transition in the susceptible–infectious–susceptible (SIS) process. Moreover, CEDMA can be further extended to depict the susceptible–infectious–recovered (SIR) process on higher-order networks.

In mobile systems or the failure detection applications, the output for some input event is state-dependent and nondeterministic after intermittent sensor failures or measurement uncertainties, which does not hold under the conventional observability hypothesis. In this article, such cases can be modeled by a Mealy-based finite-state machine (FSM) with nondeterministic output functions, and we investigate the “initial-state” observability by use of matrix semitensor product (matrix-STP). First, to characterize the nondeterministic output functions, a virtual state set consisting of state–event pairs is introduced to obtain an augmented FSM. By resorting to the matrix-STP, the algebraic expression of augmented FSM is proposed. Subsequently, based on the newly constructed model, the initial-state observability can be verified by checking the distinguishability of state trajectories of the augmented FSM. Meanwhile, the necessary and sufficient condition for such initial-state observability is derived from a discriminant matrix consisting of polynomial elements. Finally, numerical examples show the validity of the proposed method. The current results are further conducive to explore the critical safety of cyber–physical systems in many real-world systems.

We propose a novel epidemic model based on two-layered multiplex networks to explore the influence of positive and negative preventive information on epidemic propagation. In the model, one layer represents a social network with positive and negative preventive information spreading competitively, while the other one denotes the physical contact network with epidemic propagation. The individuals who are aware of positive prevention will take more effective measures to avoid being infected than those who are aware of negative prevention. Taking the microscopic Markov chain (MMC) approach, we analytically derive the expression of the epidemic threshold for the proposed epidemic model, which indicates that the diffusion of positive and negative prevention information, as well as the topology of the physical contact network have a significant impact on the epidemic threshold. By comparing the results obtained with MMC and those with the Monte Carlo (MC) simulations, it is found that they are in good agreement, but MMC can well describe the dynamics of the proposed model. Meanwhile, through extensive simulations, we demonstrate the impact of positive and negative preventive information on the epidemic threshold, as well as the prevalence of infectious diseases. We also find that the epidemic prevalence and the epidemic outbreaks can be suppressed by the diffusion of positive preventive information and be promoted by the diffusion of negative preventive information.

Networked finite state machine takes into account communication losses in industrial communication interfaces due to the limited bandwidth. The reachability analysis of networked finite state machine is a fundamental and important research topic in blocking detection, safety analysis, communication system design and so on. This paper is concerned with the impact of arbitrary communication losses on the reachability of networked finite state machine from a switched perspective. First, to model the dynamics under arbitrary communication losses in communication interfaces (from the controller to the actuator), by resorting to the semi-tensor product (STP) of matrices, a switched algebraic model of networked finite state machine with arbitrary communication losses is proposed, and the reachability analysis can be investigated by using the constructed model under arbitrary switching signal. Subsequently, based on the algebraic expression and its transition matrix, necessary and sufficient conditions for the reachability are derived for networked finite state machine. Finally, some typical numerical examples are exploited to demonstrate the effectiveness of the proposed approach. Note that current results provide valuable clues to design reliable and convergent Internet-of-Things networks.

We present a multi-layer network propagation model including both offline and online social networks, which aims to imitate the interaction between the offline actual individuals and the online social networking ones throughout the propagation process. After that, we utilize the improved SIR model to simulate the transmission in social networks under the impact of actual individuals. In our model, the individual layer adopts the generalized linear threshold model, while the social network layer uses the improved SIR model proposed in this paper. We apply these two propagation models into a three-layer network with inter-layer links, and use Monte Carlo simulation to analyze the model dynamic properties. Furthermore, we make use of mean-field approximations to obtain the analytical solutions to the critical thresholds regarding the epidemic process. We discuss the effect of different factors on the model results, and observe whether the model has different dynamic performance from the classical SIR model as well. The present results will provide some deeper insights into how various contagion phenomena spread within many real-world networks.

Attack vulnerability is one of the fundamental properties of complex interdependent networks, which has attracted a lot of research efforts in recent years. In this paper, we study the effect of degree heterogeneity on structural vulnerability of interdependent networks when they suffer targeted attacks. Firstly, we construct an interdependent system model composed of two network components. By adjusting a parameter, the extent of degree heterogeneity of each network can be controlled. Then, numerical simulations are implemented to demonstrate the impact of degree heterogeneity. The research results verify that the vulnerability of both single and interdependent networks can be affected by degree heterogeneity, that is, degree heterogeneity can significantly increase the vulnerability of these networks. Additionally, the existence of interdependent links between two networks makes both networks much more vulnerable against targeted attacks. In particular, when coupling preference is taken into account, it is found that compared with disassortative coupling and random coupling, assortative coupling can lead to a more fragile interdependent system. Our research results can give some help on the deep understanding of structural vulnerability of complex interdependent networks, and shed some light on the design of robust systems.

In this paper, we propose a novel mechanism to promote the evolution of cooperation in the spatial public goods games, in which any focal player will have a higher probability to imitate the more successful nearest neighbor. Large quantities of numerical simulations indicate that cooperation behavior will be largely changed. For a positive neighbor selection parameter (w > 0), it can be observed that the cooperation can be promoted; whereas w0 will play a crucial role during the process of cooperation for spatial public goods games. Thus, the results strongly demonstrate that coveting the more successful neighbor will foster the evolution of cooperation. The present model will be conducive to illustrating the collective cooperation phenomenon widely existing among many biological systems and artificial social societies.