Multiplex networks dynamics

In a recently proposed model (H. T. Diep, M. Kaufman, S. Kaufman, Physica A, 469, 183-199, 2017), we described the dynamics of interacting groups of individuals, such as might take place around a public decision. In this model, individuals of a given group interact with each other (intra-network), and also with individuals in other groups (across the networks). In each group, each individual has a preference, conceptualized as a (spin-like) variable s. A pair of individuals i, j within a group contributes -s_i*s_j to the intra-group energy. The inter-group energy of an individual i is taken to be proportional to the product between the preference s_i and the mean value of the preferences of the other group’s members. The noise in this system is quantified by the temperature T. We discuss the dynamics of the equivalent-neighbor networks where everyone interacts with everyone else. We explore the effect of the network topology by means of Monte-Carlo simulations on networks with short-range interactions. We also examine the dynamic consequences of adding a third group to the initial two.