arXiv subjects

Long Wang

Publications and source records attributed to Long Wang.

At least 289 records · Page 16Linked to original sources

arXiv2007

Information propagation and collective consensus in blogosphere: a game-theoretical approach

In this paper, we study the information propagation in an empirical blogging network by game-theoretical approach. The blogging network has small-world property and is scale-free. Individuals in the blogosphere coordinate their decisions according to their idiosyncratic preferences and the choices of their neighbors. We find that corresponding to different initial conditions and weights, the equilibrium frequency of discussions has a transition from high to low as a result of the common interest in the topics specified by payoff matrices. Furthermore, under recommendation, namely, individuals in blogging networks refer to additional bloggers' resources besides their nearest neighbors preferentially according to the popularity of the blogs, the whole blogging network ultrafastly evolves into consensus state (absorbing state). Our results reflect the dynamic pattern of information propagation in blogging networks.

physics.soc-ph↗

arXiv2007

Evolutionary game dynamics in inhomogeneous populations

To our knowledge, the populations are generally assumed to be homogeneous in the traditional approach to evolutionary game dynamics. Here, we focus on the inhomogeneous populations. A simple model which can describe the inhomogeneity of the populations and a microscopic process which is similar to Moran Process are presented. By studying the replicator dynamics, it is shown that this model also keeps the fixed points unchanged and can affect the speed of converging to the equilibrium state. The fixation probability and the fixation time of this model are computed and discussed. In the inhomogeneous populations, there are different situations that characterize the time scale of evolution; and in each situation, there exists an optimum solution for the time to the equilibrium points, respectively. Moreover, these results on the speed of evolution are valid for infinite and finite populations.

physics.soc-ph↗

arXiv2007

Prisoner's Dilemma on community networks

We introduce a community network model which exhibits scale-free property and study the evolutionary Prisoner's Dilemma game (PDG) on this network model. It is found that the frequency of cooperators decreases with the increment of the average degree $\bar{k}$ from the simulation results. And reducing inter-community links can promote cooperation when we keep the total links (including inner-community and inter-community links) unchanged. It is also shown that the heterogeneity of networks does not always enhance cooperation and the pattern of links among all the vertices under a given degree-distribution plays a crucial role in the dominance of cooperation in the network model.

physics.soc-ph↗

arXiv2007

Promotion of cooperation induced by the interplay between structure and game dynamics

We consider the coupled dynamics of the adaption of network structure and the evolution of strategies played by individuals occupying the network vertices. We propose a computational model in which each agent plays a $n$-round Prisoner's Dilemma game with its immediate neighbors, after that, based upon self-interest, partial individuals may punish their defective neighbors by dismissing the social tie to the one who defects the most times, meanwhile seek for a new partner at random from the neighbors of the punished agent. It is found that the promotion of cooperation is attributed to the entangled evolution of individual strategy and network structure. Moreover, we show that the emerging social networks exhibit high heterogeneity and disassortative mixing pattern. For a given average connectivity of the population and the number of rounds, there is a critical value for the fraction of individuals adapting their social interactions, above which cooperators wipe out defectors. Besides, the effects of the average degree, the number of rounds, and the intensity of selection are investigated by extensive numerical simulations. Our results to some extent reflect the underlying mechanism promoting cooperation.

physics.soc-ph↗

arXiv2007

Social dilemmas in an online social network: the structure and evolution of cooperation

We investigate two paradigms for studying the evolution of cooperation--Prisoner's Dilemma and Snowdrift game in an online friendship network obtained from a social networking site. We demonstrate that such social network has small-world property and degree distribution has a power-law tail. Besides, it has hierarchical organizations and exhibits disassortative mixing pattern. We study the evolutionary version of the two types of games on it. It is found that enhancement and sustainment of cooperative behaviors are attributable to the underlying network topological organization. It is also shown that cooperators can survive when confronted with the invasion of defectors throughout the entire ranges of parameters of both games. The evolution of cooperation on empirical networks is influenced by various network effects in a combined manner, compared with that on model networks. Our results can help understand the cooperative behaviors in human groups and society.

physics.soc-ph↗

arXiv2007

Influence of initial distributions on robust cooperation in evolutionary Prisoner's Dilemma

We study the evolutionary Prisoner's Dilemma game on scale-free networks for different initial distributions. We consider three types of initial distributions for cooperators and defectors: initially random distribution with different frequencies of defectors; intentional organization with defectors initially occupying the most connected nodes with different fractions of defectors; intentional assignment for cooperators occupying the most connected nodes with different proportions of defectors at the beginning. It is shown that initial configurations for cooperators and defectors can influence the stationary level of cooperation and the evolution speed of cooperation. Organizations with the vertices with highest connectivity representing individuals cooperators could exhibit the most robust cooperation and drive evolutionary process to converge fastest to the high steady cooperation in the three situations of initial distributions. Otherwise, we determine the critical initial frequencies of defectors above which the extinction of cooperators occurs for the respective initial distributions, and find that the presence of network loops and clusters for cooperators can favor the emergence of cooperation.

physics.soc-ph↗

arXiv2007

Evolutionary Prisoner's Dilemma on heterogeneous Newman-Watts small-world network

We focus on the heterogeneity of social networks and its role to the emergence of prevailing cooperation and sustaining cooperators. The social networks are representative of the interaction relationships between players and their encounters in each round of games. We study an evolutionary Prisoner's Dilemma game on a variant of Watts-Strogatz small-world network, whose heterogeneity can be tuned by a parameter. It is found that optimal cooperation level exists at some intermediate topological heterogeneity for different temptations to defect. Moreover, neither the most heterogeneous case nor the most homogeneous one would favor the cooperators. At intermediate heterogeneity in degree sequences, cooperators could resist the invasion of defectors for large temptation to defect.

math.DS↗

arXiv2007

Finite-Time Consensus Problems for Networks of Dynamic Agents

In this paper, finite-time state consensus problems for continuous-time multi-agent systems are discussed, and two distributive protocols, which ensure that the states of agents reach an agreement in a finite time, are presented. By employing the method of finite-time Lyapunov functions, we derive conditions that guarantee the two protocols to solve the finite-time consensus problems respectively. Moreover, one of the two protocols solves the finite-time weighted-average consensus problem and can be successively applied to the systems with switching topology. Upper bounds of convergence times are also established. Simulations are presented to show the effectiveness of our results.

math.DS↗

arXiv2006

State Agreement in Finite Time

In this paper, we consider finite-time state agreement problems for continuous-time multi-agent systems and propose two protocols, which ensure that states of agents reach an agreement in a finite time. Moreover, the second protocol solves the finite-time average-agreement problem and can be applied to the systems with switching topology. Upper bounds of convergence time are also established. Examples are presented to show the effectiveness of our results.

math.DS↗

arXiv2006

Asynchronous Consensus in Continuous-Time Multi-Agent Systems With Switching Topology and Time-Varying Delays

In this paper, we study asynchronous consensus problems of continuous-time multi-agent systems with discontinuous information transmission. The proposed consensus control strategy is implemented only based on the state information at some discrete times of each agent's neighbors. The asynchronization means that each agent's update times, at which the agent adjusts its dynamics, are independent of others'. Furthermore, it is assumed that the communication topology among agents is time-dependent and the information transmission is with bounded time-varying delays. If the union of the communication topology across any time interval with some given length contains a spanning tree, the consensus problem is shown to be solvable. The analysis tool developed in this paper is based on the nonnegative matrix theory and graph theory. The main contribution of this paper is to provide a valid distributed consensus algorithm that overcomes the difficulties caused by unreliable communication channels, such as intermittent information transmission, switching communication topology, and time-varying communication delays, and therefore has its obvious practical applications. Simulation examples are provided to demonstrate the effectiveness of our theoretical results.

math.DS↗

arXiv2006

Easily Testable Necessary and Sufficient Algebraic Criteria for Delay-independent Stability of a Class of Neutral Differential Systems

This paper analyzes the eigenvalue distribution of neutral differential systems and the corresponding difference systems, and establishes the relationship between the eigenvalue distribution and delay-independent stability of neutral differential systems. By using the ``Complete Discrimination System for Polynomials", easily testable necessary and sufficient algebraic criteria for delay-independent stability of a class of neutral differential systems are established. The algebraic criteria generalize and unify the relevant results in the literature. Moreover, the maximal delay bound guaranteeing stability can be determined if the systems are not delay-independent stable. Some numerical examples are provided to illustrate the effectiveness of our results.

math.DS↗

arXiv2006

The structure of self-organized blogosphere

In this paper, a statistical analysis of the structure of one blog community, a kind of social networks, is presented. The quantities such as degree distribution, clustering coefficient, average shortest path length are calculated to capture the features of the blogging network. We demonstrate that the blogging network has small-world property and the in and out degree distributions have power-law forms. The analysis also confirms that blogging networks show in general disassortative mixing pattern. Furthermore, the popularity of the blogs is investigated to have a Zipf's law, namely, the fraction of the number of page views of blogs follows a power law.

math.ST↗

arXiv2006

Solution to the Generalized Champagne Problem on Simultaneous Stabilization of Linear Systems

The well-known "Generalized Champagne Problem" on simultaneous stabilization of linear systems is solved by using complex analysis \cite{A73,C78,G69,N52,R87} and Blondel's technique \cite{B94,BG93,BGMR94}. We give a complete answer to the open problem proposed by Patel et al. \cite{P99,PDV02}, which automatically includes the solution to the original "Champagne Problem" \cite{BG93,BGMR94,BSVW99,LKZ99,P99,PDV02}. Based on the recent development in automated inequality-type theorem proving \cite{Y98,Y99,YHX01,YX05,YX03}, a new stabilizing controller design method is established. Our numerical examples significantly improve the relevant results in the literature \cite{LKZ99,PDV02}.

math.DS↗

arXiv2006

Information propagation in a novel hierarchical network

A novel hierarchical model of complex network is proposed, and information propagation process taking place on top of the network is investigated. Our model is demonstrated to have small world property. We found that the frequency distribution of refractory elements number is bimodal and the location of initially chosen seed infection affects the spreading range of the information.

math.DS↗

arXiv2005

Algebraic Characterizations of Consensus Problems for Networked Dynamic Systems

In this paper, we study the consensus problem for networked dynamic systems with arbitrary initial states, and present some structural characterization and direct construction of consensus functions. For the consensus problem under similar transformation, we establish some necessary and sufficient conditions by exploiting the structure of consensus functions. Finally, we discuss the consensus problem for dynamic systems under switching by using the common Lyapunov function method.

math.ST↗

arXiv2005

On Robust Stability of Multivariable Interval Control Systems

This paper studies robustness of MIMO control systems with parametric uncertainties, and establishes a lower dimensional robust stability criterion. For control systems with interval transfer matrices, we identify the minimal testing set whose stability can guarantee the stability of the entire uncertain set. Our results improve the results in the literature, and provide a constructive solution to the robustness of a family of MIMO control systems.

math.ST↗

arXiv2005

Coordination of Multiple Dynamic Agents with Asymmetric Interactions

In this paper, we consider multiple mobile agents moving in Euclidean space with point mass dynamics. Using a coordination control scheme, we can make the group generate stable flocking motion. The control laws are a combination of attractive/repulsive and alignment forces, and the control law acting on each agent relies on the position information of all agents in the group and the velocity information of its neighbors. By using the control laws, all agent velocities become asymptotically the same, collisions can be avoided between all agents, and the final tight formation minimizes all agent global potentials. Moreover, we show that the velocity of the center of mass is invariant and is equal to the final common velocity. Furthermore, we study the motion of the group when the velocity damping is taken into account. We prove that the common velocity asymptotically approaches zero, and the final configuration minimizes the global potential of all agents. In this case, we can properly modify the control scheme to generate the same stable flocking. Finally, we provide some numerical simulations to further illustrate our results.

math.ST↗

arXiv2005

Flocking Control of Groups of Mobile Autonomous Agents via Local Feedback

This paper considers a group of mobile autonomous agents moving in Euclidean space with point mass dynamics. We introduce a set of coordination control laws that enable the group to generate the desired stable flocking motion. The control laws are a combination of attractive/repulsive and alignment forces. By using the control laws, all agent velocities asymptotically approach the desired velocity, collisions can be avoided between agents, and the final tight formation minimizes all agent potentials. Moreover, we prove that the velocity of the center of mass is always equal to the desired velocity or exponentially converges to the desired value. Furthermore, we study the motion of the group when the velocity damping is taken into account. In this case, we can properly modify the control laws to generate the same stable flocking motion. Finally, for the case that not all agents know the desired final velocity, we show that the desired flocking motion can still be obtained. Numerical simulations are worked out to illustrate our theoretical results.

math.ST↗