Mathematical methods in the study of political conflicts: parametric estimation model

This study aims to develop a comprehensive parametric model for quantifying and predicting political conflicts through mathematical analysis. It addresses the need for objective tools to assess the intensity, dynamics, and potential development trajectories of conflicts across different scales of political confrontation. The research employs an integrated analytical framework that combines discrete dynamical systems, parametric modeling, and stability analysis to construct a robust mathematical apparatus. The model is based on a system of difference equations describing the interactions among key conflict parameters-confrontation intensity, resource potential of parties, external influences, and socio-political context. An integral indicator of conflict intensity is introduced, using weighted coefficients of parameter significance to account for both explicit and latent factors. Stability analysis of the system identifies conditions under which political conflicts tend toward resolution or escalation. The study finds that sustainable conflict resolution occurs when cross-response parameters (mutual reactions between parties) exceed self-response parameters (reactions to one's own conflict situation). Behavioral strategies are expressed through linear relationships that capture how parties adapt their approaches in response to their own and their opponents' actions. These findings highlight that empathy, strategic consideration of opponents, and interdependent behavioral dynamics are essential factors in achieving conflict resolution. Validation through case studies - such as wage disputes and social movements - demonstrates the model's effectiveness in analyzing complex socio-political processes. The study concludes with practical recommendations for implementing the model in analytical centers and government agencies to support evidence-based conflict management strategies.