Modified Krasnoshchekov model in case of the reducible matrix of social interactions

In this paper Krasnoshchekov’s model, describing the behavior of people in the community under social and informational influences, is extended in the case of the system, having the sophisticated structure of social interactions. In particular, the situation in which is formed an isolated group of people, unfamiliar with the rest of the community, which corresponds to the decomposability of the matrix of social interactions is under consideration. Conditions of the existence and uniqueness solution of the equations, describing the behavior of such a community are investigated. The problem of the connection between Krasnoshchekov’s and De Groot’s model is fixed. The way, how the above matrix and social independence of individuals affect on the solution of this system structure, which describes, in particular, the spread of beliefs among the people is also investigated.