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Converging and emerging behavior of different phenomena call for a strong tool to describe the behavior of mutli-agent systems. Economics and quantitative sociology are two of the most important areas where these behavioral patterns are observed. In this paper, a brief introduction to statistical physics is provided as a tool to understand and investigate the upper-mentioned phenomena. Some of the available interaction models used in quantitative sociology have been presented to get an idea of how they work. Using one of these models, a discrete nonlinear dynamic system is presented. Main focus of this paper is providing necessary tools and solutions for discrete nonlinear dynamical systems.