Binary opinion dynamics with noise on random networks

Abstract

Two kinds of noise strategies in binary opinion dynamics on ER random networks are discussed. Random noise p 1 in the initial configuration plays a role in redistributing the opinion states associated with the network. Under synchronous updating, the system can attain a stable state within few time steps. The fraction of nodes with changed opinion states F decreases exponentially with time, and the ratio of one of the two opinion states R remains almost unchanged during the evolution. The average ratio <R> crosses at the half-half initial concentration under different p 1 . For noise in the dynamical evolution p 2 , the system can reach a steady state with small fluctuations. With larger p 2 , more nodes have changed opinion states at each updating and more nodes with opposite opinions coexist. If p 2 is greater than 0.5, the two opinions coexist with equal support. binary opinion dynamics, random noise, complex networks Citation:Chi L P. Binary opinion dynamics with noise on random networks. Chinese Sci Bull, 2011, 56: 36303632, doi: 10.1007/s11434-011-4751-1In recent years, much effort has been invested in social dynamics formulated with concepts and methods from statistical physics [1][2][3]. Opinion dynamics is one of the social problems well-studied by physicists based on the famous Ising model from three decades ago [4]. Since then, quite a few opinion models have been proposed, such as the voter model [5,6], the Sznajd model [7][8][9][10][11][12][13] and the bounded confidence model [14][15][16], to name a few. In most of these models, each of N agents is assigned a finite number of available states of opinions. Opinion formation is modeled as a collective behavior of agents in which individuals evolve following either majority rule or imitation. In a binary opinion dynamics, two competing states, +1 or 1, are considered. Despite the complex dynamics of opinions among agents, the system attains total consensus of one of the two contrasting opinions, or a steady state with an equal distribution of opinions. The growing field of complex networks [17][18][19][20][21][22] enables us to obtain a better knowledge of social systems. The intense theoretical research currently taking place, examines the systems of nodes representing agents and links representing the interactions between them. In the random network proposed by Erdos and Renyi (ER), N nodes are connected by n edges selected randomly from the N(N1)/2 possible edges; the connection probability is p = n/N(N1)/2. The number k of edges connecting one node to others is called the degree of that node. The average degree of the random network is <k>=2n/N = p(N1)≈pN if p<<1.The aim of our model in this paper is to explore the evolution and to determine the final state of the binary opinion dynamics with noise. The opinion dynamics is performed on the ER random network with nodes N = 10 5 and average degree <k>=4. In the initial configuration, each node is assigned an opinion 1 with probability f and +1 with probability 1f. In this binary opinion dynam...

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