Deterministic Multicultural Dynamic Networks: Seeking a Balance between Attractive and Repulsive Forces

Abstract

An important issue in society is the attempt to balance communities working co-operatively and cohesively with one another while allowing members the ability to retain individuality and fostering an environment of cultural diversity. We seek to study the cohesive properties of a culturally diverse dynamic social network. By considering a multi-agent dynamic network, we seek to model a social structure and find conditions under which cohesion and coexistence are maintained. We present a specific illustration that serves to establish the framework in which explicit sufficient conditions in terms of system parameters are found for which the network is cohesive. By utilizing Lyapunov’s Second Method and comparison equations, we are able to find such conditions for the given illustration. Further, for the illustration, we decompose the cultural state domain into invariant sets and consider the behavior of members within each set. Moreover, we analyze the relative cultural affinity between individual members relative to the center of the social network. We also demonstrate how conservative the estimates are using Euler type numerical approximation schemes based on the given illustration. We are then able to consider how changes in the various parameters affect the dynamics of the illustrated network. By gaining such insight into the behavior of the illustrated network, we are able to better understand the impact of both attractive and repulsive influences on the network. This leads to establishing a schema for helping when creating policies and practices catered to promoting both diversity and cohesion within a cultural network.