Co-evolution of heterogeneous cognition in spatial snowdrift game with asymmetric cost.

The emergence of the evolutionary game on complex networks provides a fresh framework for studying cooperation behavior between complex populations. Numerous recent progress has been achieved in studying asymmetric games. However, there is still a substantial need to address how to flexibly express the individual asymmetric nature. In this paper, we employ mutual cognition among individuals to elucidate the asymmetry inherent in their interactions. Cognition arises from individuals' subjective assessments and significantly influences their decision-making processes. In social networks, mutual cognition among individuals is a persistent phenomenon and frequently displays heterogeneity as the influence of their interactions. This unequal cognitive dynamic will, in turn, influence the interactions, culminating in asymmetric outcomes. To better illustrate the inter-individual cognition in asymmetric snowdrift games, the concept of favor value is introduced here. On this basis, the evolution of cognition and its relationship with asymmetry degree are defined. In our simulation, we investigate how game cost and the intensity of individual cognitive changes impact the cooperation frequency. Furthermore, the temporal evolution of individual cognition and its variation under different parameters was also examined. The simulation results reveal that the emergence of heterogeneous cognition effectively addresses social dilemmas, with asymmetric interactions among individuals enhancing the propensity for cooperative choices. It is noteworthy that distinctions exist in the rules governing cooperation and cognitive evolution between regular networks and Watts-Strogatz small-world networks. In light of this, we deduce the relationship between cognition evolution and cooperative behavior in co-evolution and explore potential factors influencing cooperation within the system.

Coevolution of relationship and interaction in cooperative dynamical multiplex networks.

While actors in a population can interact with anyone else freely, social relations significantly influence our inclination toward particular individuals. The consequence of such interactions, however, may also form the intensity of our relations established earlier. These dynamical processes are captured via a coevolutionary model staged in multiplex networks with two distinct layers. In a so-called relationship layer, the weights of edges among players may change in time as a consequence of games played in the alternative interaction layer. As an reasonable assumption, bilateral cooperation confirms while mutual defection weakens these weight factors. Importantly, the fitness of a player, which basically determines the success of a strategy imitation, depends not only on the payoff collected from interactions, but also on the individual relationship index calculated from the mentioned weight factors of related edges. Within the framework of weak prisoner's dilemma situation, we explore the potential outcomes of the mentioned coevolutionary process where we assume different topologies for relationship layer. We find that higher average degree of the relationship graph is more beneficial to maintain cooperation in regular graphs, but the randomness of links could be a decisive factor in harsh situations. Surprisingly, a stronger coupling between relationship index and fitness discourage the evolution of cooperation by weakening the direct consequence of a strategy change. To complete our study, we also monitor how the distribution of relationship index vary and detect a strong relation between its polarization and the general cooperation level.

Signal and Information Processing in Networks.

Networks are omnipresent in the realm of science, serving as a central focus in our modern world [...].

Inhibition and activation of interactions in networked weak prisoner's dilemma.

In the framework of the coevolution dynamics of the weak prisoner's dilemma, inspired by prior empirical research, we present a coevolutionary model with local network dynamics in a static network framework. Viewing the edges of the network as social interactions between individuals, when individuals play the weak prisoner's dilemma game, they accumulate both payoffs and social interaction willingness based on a payoff matrix of the social interaction willingness we constructed. The edges are then inhibiting or activating based on the social interaction willingness of the two individuals, and individuals only interact with others through activated edges, resulting in local network dynamics in a static network framework. Individuals who receive more cooperation will be more likely to activate the edges around them, meaning they will participate in more social interactions. Conversely, individuals who receive more defects will do the opposite. Specifically, we investigate the evolutionary dynamics of cooperation under different levels of sensitivity to social interaction willingness and the temptation to defect. Through the simulation, we find that sparse cooperator clusters can expand greatly when social interaction sensitivity and temptation to defect are low. In contrast, dense cooperator clusters form rapidly in a high social interaction sensitivity, which protects the cooperation from high temptation.

The impact of nodes of information dissemination on epidemic spreading in dynamic multiplex networks.

Epidemic spreading processes on dynamic multiplex networks provide a more accurate description of natural spreading processes than those on single layered networks. To describe the influence of different individuals in the awareness layer on epidemic spreading, we propose a two-layer network-based epidemic spreading model, including some individuals who neglect the epidemic, and we explore how individuals with different properties in the awareness layer will affect the spread of epidemics. The two-layer network model is divided into an information transmission layer and a disease spreading layer. Each node in the layer represents an individual with different connections in different layers. Individuals with awareness will be infected with a lower probability compared to unaware individuals, which corresponds to the various epidemic prevention measures in real life. We adopt the micro-Markov chain approach to analytically derive the threshold for the proposed epidemic model, which demonstrates that the awareness layer affects the threshold of disease spreading. We then explore how individuals with different properties would affect the disease spreading process through extensive Monte Carlo numerical simulations. We find that individuals with high centrality in the awareness layer would significantly inhibit the transmission of infectious diseases. Additionally, we propose conjectures and explanations for the approximately linear effect of individuals with low centrality in the awareness layer on the number of infected individuals.

Network spreading among areas: A dynamical complex network modeling approach.

With the outbreak of COVID-19, great loss and damage were brought to human society, making the study of epidemic spreading become a significant topic nowadays. To analyze the spread of infectious diseases among different areas, e.g., communities, cities, or countries, we construct a network, based on the epidemic model and the network coupling, whose nodes denote areas, and edges represent population migrations between two areas. Each node follows its dynamic, which describes an epidemic spreading among individuals in an area, and the node also interacts with other nodes, which indicates the spreading among different areas. By giving mathematical proof, we deduce that our model has a stable solution despite the network structure. We propose the peak infected ratio (PIR) as a property of infectious diseases in a certain area, which is not independent of the network structure. We find that increasing the population mobility or the disease infectiousness both cause higher peak infected population all over different by simulation. Furthermore, we apply our model to real-world data on COVID-19 and after properly adjusting the parameters of our model, the distribution of the peak infection ratio in different areas can be well fitted.

Effect of local and global information on the dynamical interplay between awareness and epidemic transmission in multiplex networks.

Recent few years have witnessed a growing interest in exploring the dynamical interplay between awareness and epidemic transmission within the framework of multiplex networks. However, both local and global information have significant impacts on individual awareness and behavior, which have not been adequately characterized in the existing works. To this end, we propose a local and global information controlled spreading model to explore the dynamics of two spreading processes. In the upper layer, we construct a threshold model to describe the awareness diffusion process and introduce local and global awareness information as variables into an individual awareness ratio. In the lower layer, we adopt the classical susceptible-infected-susceptible model to represent the epidemic propagation process and introduce local and global epidemic information into individual precaution degree to reflect individual heterogeneity. Using the microscopic Markov chain approach, we theoretically derive the threshold for epidemic outbreaks. Our findings suggest that the local and global information can motivate individuals to increase self-protection awareness and take more precaution measures, thereby reducing disease infection probability and suppressing the spread of epidemics.

Spatial evolution of cooperation with variable payoffs.

In the evolution of cooperation, the individuals' payoffs are commonly random in real situations, e.g., the social networks and the economic regions, leading to unpredictable factors. Therefore, there are chances for each individual to obtain the exceeding payoff and risks to get the low payoff. In this paper, we consider that each individual's payoff follows a specific probability distribution with a fixed expectation, where the normal distribution and the exponential distribution are employed in our model. In the simulations, we perform the models on the weak prisoner's dilemmas (WPDs) and the snowdrift games (SDGs), and four types of networks, including the hexagon lattice, the square lattice, the small-world network, and the triangular lattice are considered. For the individuals' normally distributed payoff, we find that the higher standard deviation usually inhibits the cooperation for the WPDs but promotes the cooperation for the SDGs. Besides, with a higher standard deviation, the cooperation clusters are usually split for the WPDs but constructed for the SDGs. For the individuals' exponentially distributed payoff, we find that the small-world network provides the best condition for the emergence of cooperators in WPDs and SDGs. However, when playing SDGs, the small-world network allows the smallest space for the pure cooperative state while the hexagon lattice allows the largest.

Prisoner's Dilemma Game with Cooperation-Defection Dominance Strategies on Correlational Multilayer Networks.

As multilayer networks are widely applied in modern society, numerous studies have shown the impact of a multilayer network structure and the network nature on the proportion of cooperators in the network. In this paper, we use Barabási-Albert scale-free networks (BA) and Watts and Strogatz networks (WS) to build a multilayer network structure, and we propose a new strategy-updating rule called "cooperation-defection dominance", which can be likened to dominant and recessive traits in biogenetics. With the newly constructed multilayer network structure and the strategy-updating rules, based on the simulation results, we find that in the BA-BA network, the cooperation dominance strategy can make the networks with different rs show a cooperative trend, while the defection dominance strategy only has an obvious effect on the network cooperation with a larger r. When the BA network is connected to the WS network, we find that the effect of strategy on the proportion of cooperators in the network decreases, and the main influencing factor is the structure of the network. In the three-layer network, the cooperation dominance strategy has a greater impact on the BA network, and the proportion of the cooperators is enhanced more than under the natural evolution strategy, but the promotion effect is still smaller than that of the two-layer BA network because of the WS network. Under the defection dominance strategy, the WS layer appears different from the first two strategies, and we conclude through simulation that when the payoff parameter is at the middle level, its cooperator proportion will be suppressed, and we deduce that the proportion of cooperators and defectors, as well as the payoff, play an important role.

Limited resource network modeling and its opinion diffusion dynamics.

The preferential attachment of the Barabási-Albert model has been playing an important role in modeling practical complex networks. The preferential attachment mechanism describes the role of many real systems, which follows the characteristic "the rich get richer." However, there are some situations that are ignored by the preferential attachment mechanism, one of which is the existence of the limited resource. Vertices with the largest degree may not obtain new edges by the highest probability due to various factors, e.g., in social relationship networks, vertices with quite a lot of relationships may not connect to new vertices since their energy and resource are limited. Hence, the limit for degree growing is proposed in our new network model. We adjust the attachment rule in light of the population growth curve in biology, which considers both attraction and restriction of the degree. In addition, the unaware-aware-unaware opinion diffusion is studied on our proposed network. The celebrity effect is taken into consideration in the opinion diffusion process.

Evolutionary multigame with conformists and profiteers based on dynamic complex networks.

Evolutionary game on complex networks provides a new research framework for analyzing and predicting group decision-making behavior in an interactive environment, in which most researchers assumed players as profiteers. However, current studies have shown that players are sometimes conformists rather than profit-seeking in society, but most research has been discussed on a simple game without considering the impact of multiple games. In this paper, we study the influence of conformists and profiteers on the evolution of cooperation in multiple games and illustrate two different strategy-updating rules based on these conformists and profiteers. Different from previous studies, we introduce a similarity between players into strategy-updating rules and explore the evolutionary game process, including the strategy updating, the transformation of players' type, and the dynamic evolution of the network structure. In the simulation, we implement our model on scale-free and regular networks and provide some explanations from the perspective of strategy transition, type transition, and network topology properties to prove the validity of our model.

Distributed event-triggered adaptive partial diffusion strategy under dynamic network topology.

In wireless sensor networks, the dynamic network topology and the limitation of communication resources may lead to degradation of the estimation performance of distributed algorithms. To solve this problem, we propose an event-triggered adaptive partial diffusion least mean-square algorithm (ET-APDLMS). On the one hand, the adaptive partial diffusion strategy adapts to the dynamic topology of the network while ensuring the estimation performance. On the other hand, the event-triggered mechanism can effectively reduce the data redundancy and save the communication resources of the network. The communication cost analysis of the ET-APDLMS algorithm is given in the performance analysis. The theoretical results prove that the algorithm is asymptotically unbiased, and it converges in the mean sense and the mean-square sense. In the simulation, we compare the mean-square deviation performance of the ET-APDLMS algorithm and other different diffusion algorithms. The simulation results are consistent with the performance analysis, which verifies the effectiveness of the proposed algorithm.

The accumulative law and its probability model: an extension of the Pareto distribution and the log-normal distribution.

The divergence between the Pareto distribution and the log-normal distribution has been observed persistently over the past couple of decades in complex network research, economics, and social sciences. To address this, we here propose an approach termed as the accumulative law and its related probability model. We show that the resulting accumulative distribution has properties that are akin to both the Pareto distribution and the log-normal distribution, which leads to a broad range of applications in modelling and fitting real data. We present all the details of the accumulative law, describe the properties of the distribution, as well as the allocation and the accumulation of variables. We also show how the proposed accumulative law can be applied to generate complex networks, to describe the accumulation of personal wealth, and to explain the scaling of internet traffic across different domains.

Evolving networks based on birth and death process regarding the scale stationarity.

Since the past few decades, scale-free networks have played an important role in studying the topologies of systems in the real world. From the traditional perspective, the scale of network, the number of nodes, keeps growing over time without decreasing, leading to the non-stationarity of the scale which is against the real networks. To address this issue, in this paper, we introduce both increase and decrease of vertices to build the evolving network models based on birth and death random processes which are regarded as queuing systems in mathematics. Besides the modeling, the scale of networks based on different random processes is also deduced to be stationary and denoted by a specific probabilistic expression irrelevant to time. In the simulations, we build our network models by different types of queueing systems and compare the statistical results with theories to show the validity and accuracy of our proposed models. Additionally, our model is applied to simulate and predict the populations of some developed countries in recent years.

Subnormal Distribution Derived From Evolving Networks With Variable Elements.

During the past decades, power-law distributions have played a significant role in analyzing the topology of scale-free networks. However, in the observation of degree distributions in practical networks and other nonuniform distributions such as the wealth distribution, we discover that, there exists a peak at the beginning of most real distributions, which cannot be accurately described by a monotonic decreasing power-law distribution. To better describe the real distributions, in this paper, we propose a subnormal distribution derived from evolving networks with variable elements and study its statistical properties for the first time. By utilizing this distribution, we can precisely describe those distributions commonly existing in the real world, e.g., distributions of degree in social networks and personal wealth. Additionally, we fit connectivity in evolving networks and the data observed in the real world by the proposed subnormal distribution, resulting in a better performance of fitness.

Evolving Scale-Free Networks by Poisson Process: Modeling and Degree Distribution.

Since the great mathematician Leonhard Euler initiated the study of graph theory, the network has been one of the most significant research subject in multidisciplinary. In recent years, the proposition of the small-world and scale-free properties of complex networks in statistical physics made the network science intriguing again for many researchers. One of the challenges of the network science is to propose rational models for complex networks. In this paper, in order to reveal the influence of the vertex generating mechanism of complex networks, we propose three novel models based on the homogeneous Poisson, nonhomogeneous Poisson and birth death process, respectively, which can be regarded as typical scale-free networks and utilized to simulate practical networks. The degree distribution and exponent are analyzed and explained in mathematics by different approaches. In the simulation, we display the modeling process, the degree distribution of empirical data by statistical methods, and reliability of proposed networks, results show our models follow the features of typical complex networks. Finally, some future challenges for complex systems are discussed.