Contrarian Majority Rule Model with External Oscillating Propaganda and Individual Inertias

GIMENEZ, MARIA CECILIA; REINAUDI, LUIS; SERGE GALAM; FEDERICO VAZQUEZ

ENTROPY

MOLECULAR DIVERSITY PRESERVATION INTERNATIONAL-MDPI

Año: 2023 vol. 25 p. 1 - 12

1099-4300

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 𝑝(𝑡) (majority behavior) or the opposite opinion with probability 1−𝑝(𝑡) (contrarian behavior). The probability of following the majority rule 𝑝(𝑡) 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 𝑇𝑐 separates a bimodal oscillatory regime for 𝑇<𝑇𝑐, where the population’s mean opinion m oscillates around a positive or a negative value from a unimodal oscillatory regime for 𝑇>𝑇𝑐 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 𝑇∗, where the response of the system is maximum. An insight into these results is given by a mean-field approach, which also shows that 𝑇∗ and 𝑇𝑐 are closely related.