Stochastic Hybrid Dynamic Multicultural Social Networks

Abstract

In this work, we investigate the cohesive properties of a stochastic hybrid dynamic multi-cultural network under random environmental perturbations. By considering a multi-agent dynamic network, we model a social structure and find conditions under which cohesion and coexistence is maintained using Lyapunov's Second Method and the comparison method. In this paper, we present a prototype illustration that exhibits the significance of the framework and approach. Moreover, the explicit sufficient conditions in terms of system parameters are given to exhibit when the network is cohesive both locally and globally. The sufficient conditions are algebraically simple, easy to verify, and robust. Further, we decompose the cultural state domain into invariant sets and consider the behavior of members within each set. We also analyze the degree of conservativeness of the estimates using Euler-Maruyama type numerical approximation schemes based on the given illustration.