Abstract
The interactions of opinions on the complex networks are significantly impacted by the structure of the networks. Previous studies of this kind mainly investigated the opinion dynamics on the fixed networks as a kind of synchronization. In this study, we focus on how the opinions evolving on the growing networks. We provide isolated nodes with different initial opinions at the beginning. The Achlioptas Process is introduced to link the nodes eventually. The opinions of two nodes influence each other linearly if there is a link between the two nodes. We establish both random graph and scale-free network in this paper. The finite-size scaling is discussed. We discover explosive transition of the speed for the opinions to achieve a consensus on some networks. Meanwhile, the stability of the networks to suppress the random damage is highly enhanced by the Achlioptas Process which is used to link all the nodes as a network. The encouraging results are obtained on different structures of networks.
Highlights
OF OPINION DYNAMICS ON EVOLVING NETWORKSOpinion dynamics, as one of the social dynamics studied extensively in recent years [1]–[4], is the dynamics of systems incorporating the evolution of two or more competing states [5] through various mathematical and statistical physics theories
The innovation of the paper include: 1) We propose a new method to establish complex networks by Achlioptas Process, which leads to the explosive transition in opinion convergence and enhances the ability against the damage to the network; 2) The ‘social outcast’ on a network makes the adjacency matrix and Laplacian matrix of the network asymmetric
We discover that the Achlioptas Process causes percolation transition of the size of the largest cluster in some growing network
Summary
As one of the social dynamics studied extensively in recent years [1]–[4], is the dynamics of systems incorporating the evolution of two or more competing states [5] through various mathematical and statistical physics theories. Some research have attempted to introduce the complex network to the area of social studies like opinion dynamics. The innovation of the paper include: 1) We propose a new method to establish complex networks by Achlioptas Process, which leads to the explosive transition in opinion convergence and enhances the ability against the damage to the network; 2) The ‘social outcast’ on a network makes the adjacency matrix and Laplacian matrix of the network asymmetric. The paper is organized as follows: In Section 2, we propose the differential-equation based opinion models on complex networks. THE ESTABLISHMENT OF THE DIFFERENTIAL-EQUATION BASED OPINION MODEL Consider a simple dynamical network consisting of N identical nodes with diffusive influence ability to each other, in which each node is an N-dimensional dynamical system.
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