Contrarian Majority Rule Model with External Oscillating Propaganda and Individual Inertias

We study the Galam majority rule dynamics with contrarian behavior and an oscillating external propaganda in a population of agents that can adopt one of two possible opinions. In an iteration step, a random agent interacts with three other random agents and takes the majority opinion among the agents with probability [Formula: see text] (majority behavior) or the opposite opinion with probability [Formula: see text] (contrarian behavior). The probability of following the majority rule [Formula: see text] varies with the temperature T and is coupled to a time-dependent oscillating field that mimics a mass media propaganda, in a way that agents are more likely to adopt the majority opinion when it is aligned with the sign of the field. We investigate the dynamics of this model on a complete graph and find various regimes as T is varied. A transition temperature [Formula: see text] separates a bimodal oscillatory regime for [Formula: see text] , where the population’s mean opinion m oscillates around a positive or a negative value from a unimodal oscillatory regime for [Formula: see text] in which m oscillates around zero. These regimes are characterized by the distribution of residence times that exhibit a unique peak for a resonance temperature [Formula: see text] , where the response of the system is maximum. An insight into these results is given by a mean-field approach, which also shows that [Formula: see text] and [Formula: see text] are closely related.