TITLE:
Deterministic Multicultural Dynamic Networks: Seeking a Balance between Attractive and Repulsive Forces
AUTHORS:
Kristina B. Hilton, G. S. Ladde
KEYWORDS:
Multi-Agent Network, Cohesiveness, Lyapunov Second Method, Invariant Sets, Social Network
JOURNAL NAME:
International Journal of Communications, Network and System Sciences,
Vol.9 No.12,
December
23,
2016
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.