Modeling of human society as a locally interacting product-potential networks of automaton

Abstract: The central problems in social sciences concern the social and psychological mechanisms and conditions required for the emergence and stability of human groups. The present article is dedicated to the problem of stability of human groups. We model human groups using local interacting systems of automaton with relations and reactions and using the structural balance theory. The 'structural balance theory' ties the emergence of a human group with the human actor's thoughts about how another actor treats him and his perception of actors. The Cartwright and Harary formalization the concept of balance theory within a graph theoretical setting unable to get a number of mathematical results pertaining to an algebraic formulation of the theory of balance in signed networks/graphs. The deeper generalization of 'balance theory' as the smooth product-potential fields on domain gives us the ability to create theory of 'smooth product potential social fields'. We then find that all discrete product-potential system tightly connect with other process - process multiplication on the randomly chosen matrices and we find connections between stationary measures and some algebraic objects.