Rumor spreading: A trigger for proliferation or fading away

Exploration-imitation competition in well-mixed and structured populations

Social physics is the mathematical study of how the flow of ideas can change the behavior of individuals. Models in social physics include processes for searching after new ideas and dispersing them inside the population. The present paper makes use of exploration and imitation processes for the mentioned purpose. A new type of imitation is employed here, in which the imitant strategy is not simply replaced by role model strategy, but rather moves toward it. Our exploration process is additive Gaussian noise. To study these processes, we both analyze and simulate the strategy distribution function. By combining exploration and soft imitation, the width of the strategy distribution function becomes stationary. In this model, regular imitation is a particular limit of soft imitation, where an imitant copies the role model, through which the stationary width of the distribution function disappears. As the network causes complex behavior, soft imitation and exploration have been studied in some complex networks as well. Simulation results show that for a small world, scale-free, random regular, and random network, and by selected parameters in this research, distribution function width reaches stationary states.

Three-state majority-vote model on small-world networks

In this work, we study the opinion dynamics of the three-state majority-vote model on small-world networks of social interactions. In the majority-vote dynamics, an individual adopts the opinion of the majority of its neighbors with probability 1-q, and a different opinion with chance q, where q stands for the noise parameter. The noise q acts as a social temperature, inducing dissent among individual opinions. With probability p, we rewire the connections of the two-dimensional square lattice network, allowing long-range interactions in the society, thus yielding the small-world property present in many different real-world systems. We investigate the degree distribution, average clustering coefficient and average shortest path length to characterize the topology of the rewired networks of social interactions. By employing Monte Carlo simulations, we investigate the second-order phase transition of the three-state majority-vote dynamics, and obtain the critical noise [Formula: see text], as well as the standard critical exponents [Formula: see text], [Formula: see text], and [Formula: see text] for several values of the rewiring probability p. We conclude that the rewiring of the lattice enhances the social order in the system and drives the model to different universality classes from that of the three-state majority-vote model in two-dimensional square lattices.