The article presents a study combining the methods of literary and linguistic text analysis of a work of fiction and methods of mathematical modeling of the plot. The purpose of the work is to study the factors that affect human relationships by creating and analyzing nonlinear dynamic systems in terms of the postulates and methods of deterministic chaos theory. The research method is to create a mathematical model of the characters’ characteristics and their relationships. The authors chose the text of the novel “Les Misérables” by V. Hugo as the research material. The main mathematical apparatus of the study is based on the methods of numerical fractal analysis; a nonlinear mathematical model based on a two-dimensional system of differential equations is established. In the process of the research, the proposed system will be integrated by numerical methods: a topologically equivalent extractor will be built to solve it using the Takens delay method. The Hurst exponent and approximated entropy are calculated to determine the future trend change of the attractor, and a bifurcation diagram is constructed using a Poincare mapping to determine a specific fractal time. By changing the parameters of the system and observing the changes in the values and graphs obtained above, we analyzed the main factors influencing social relationships from the perspective of sociology, psychology, and history. At the same time, in the process of the research we will focus on three factors: the personality itself, the influence of related characters, and the literary projection of the social environment.