Stimulus-driven consensus of allelomimetic agents in a confined lattice environment

Abstract

In this paper, we investigate the dynamics of opinion formation in a confined lattice system where there prevail two kinds of state or opinion and whose agents are characterized by an allelomimetic tendency α (that is, the probability of imitating the majority state within a circular neighborhood with radius r). Unlike most opinion dynamics models, an agent otherwise migrates to a random empty site in its von Neumann neighborhood, which corresponds to its four nearest neighboring sites, with probability 1 - α (called the migratory tendency in this study). We have observed an early steady-state for the number of transitions from one state to another in the system for values of α close to 1 for constant r. In addition, greater number of transitions occurs for small values of r. Moreover, opinion fragmentation takes place in the system which is represented by the formation of homogenous clusters.