|Title||STOCHASTIC MULTICULTURAL DYNAMIC NETWORKS|
|Publication Type||Journal Article|
|Year of Publication||2017|
|Authors||HILTON KRISTINA, LADDE G.|
|Journal||Dynamic Systems and Applications|
|AMS Subject Classification||37H10|
In this work, we seek to study the cohesive properties of a dynamic multi-cultural network under random environmental perturbations. By considering a multi-agent dynamic network, we seek to model a social structure and find conditions under which cohesion and coexistence is maintained. Utilizing Lyapunov’s Second Method and the comparison method, we present a prototype illustration which serves 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. 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 demonstrate how conservative the estimates are using Euler-Maruyama type numerical approximation schemes based on the given illustration.