A stochastic quenched disorder model for interaction of network-master node systems

Abstract

Human beings live in a networked world in which information spreads very fast thanks to advances in technology. This helps to promote conflicts that lead to the dominance of certain ideologies, set of values, belief or opinion. Such conflicts can lead to a decrease in freedom, oppression and to the deterioration of established institutions. Here, we propose a simple model to study, to a certain extent, this class of problems. We look at interacting agents connected in networks to analyze the multi-agent decision stochastic process. Each individual decision may be influenced by others’ decisions. We consider a first neighbor interaction between agents in one-dimensional network. Some agents are also connected to a hub, or master node, who has preferential opinions. The role of the master node is to persuade others to follow a specific orientation, in which there is a probability of successful persuasion. The connections between master node and the network society are quenched disorder. Using a simple model, we found a phase transition from disorder to order for three different control parameters. The evidence for the phase transition in the model was obtained by finite-size scaling analysis. In addition, we present an analytical result via the mean-field approximation. Finally, we discuss how this model may be useful as a framework to study the spread of morality, innovation, opinion formation and consensus.