Improved Finite Time in Eliminating Disagreement of Opinion Dynamics via Noise

Yong Ding,Lipo Mo

doi:10.1155/2017/1098169

Abstract

We aim to refine the estimation of the finite stopping time when the disagreement in an opinion group is eliminated by a simple but novel noise intervened strategy. It has been proved that, by using this noise intervened control strategy, the divisive opinions would get synchronized in finite time. Moreover, the finite stopping time when resolving the disagreement has been clarified. The estimation of the finite stopping time will effectively reveal which factors and how they determine the consequence of intervention. However, the upper bound for the estimation of the integrable stopping time when noise is oriented has been quite conservative. In this paper, we investigate the finite stopping time of eliminating the disagreement by completely oriented noise and a much more precise formula for the estimation of the finite stopping time is obtained finally via direct calculation.

Highlights

In the recent decades, modeling and analysis of opinion dynamics are becoming a much attractive area
More and more researchers from various fields have paid attention to it [1, 2], and several agent-based mathematical models have been established to investigate the evolution of opinion dynamics [3,4,5,6,7,8,9,10,11,12,13]
The evolution of the opinions can be determined by the interaction topology of agents which are based on the preassumed graph or the bounded confidence (BC) of the agents

Summary

Introduction

In the recent decades, modeling and analysis of opinion dynamics are becoming a much attractive area. In [23], based on the well-known Hegselmann-Krause (HK) confidence model, it was strictly proved that the noise could almost surely induce the opinions to achieve quasi-consensus in finite time, and the critical noise strength is obtained. These results reveal the richer mechanisms of the opinion evolution, and provide new insights into designing noise intervention strategy to eliminate the disagreement in a group.

Basic Model and Preliminaries

Main Results

Simulations

Conclusions