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This work deals with the development of multi-cultural network-centric dynamic models under the influence of personal intra- and inter-members, as well as community. Each individual member of a society is influenced by her/his interactions with fellow members of the family, neighborhood, region and the universe. The behavior of such complex and highly interacting social networks is characterized by stochastic interconnected dynamical systems. The primary goal is on laying down an investigation of both qualitative and quantitative properties of this network dynamical system. In particular, we would like to determine the regions of conflicts and coexietence as well as to establish the cohesion and stability of emerging states. This is achieved by employing the method of system of differential inequalities and comparison theorems in the context of the energy function. The developed energy function method provides estimates for regions of conflict and cooperation. Moreover, the method also provides sufficient conditions for the community cohesion and stability in a systematic way.