Stochastic Hybrid Dynamic Multicultural Social Networks

  • Kristina Buzzell Hilton Department of Mathematics and Statistics, University of South Florida, Tampa, FL, United States;
  • G. S. Ladde Department of Mathematics and Statistics, University of South Florida, Tampa, FL, United States;
Keywords: Multi-agent Network, Cohesiveness, Lyapunov Second Method, Invariant Sets

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.

Author Biographies

Kristina Buzzell Hilton, Department of Mathematics and Statistics, University of South Florida, Tampa, FL, United States;

Department of Mathematics and Statistics

University of South Florida

G. S. Ladde, Department of Mathematics and Statistics, University of South Florida, Tampa, FL, United States;

Department of Mathematics and Statistics

Professor

University of South Florida

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Published
2017-11-08