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The authors propose a model of nonlinear interaction of social network agents, which is based on a matrix generalization of the known one-dimensional logistic mapping. Similar models have not been considered previously and have not been investigated numerically. Despite the relative simplicity of the proposed non-linear model, in the course of numerical experiments, various modes of agent behavior were observed. Namely, one of the agents hesitated in making a certain decision, others were able to "agree" (came to ...