Quantitative Analysis of Dynamic Systems: Interaction Models Through Differential Equations

Abstract

This article explores the quantitative analysis of interacting dynamic systems using differential equations. Specifically, this approach is applied to model a hypothetical two-sided confrontation. The power potential and effectiveness of each side are taken into account, and the system dynamics and its evolution over time are determined through mathematical methods. Simulation results indicate that the side with higher efficiency coefficients wins the upper hand. The duration of the conflict and the resource losses for each side are assessed, revealing that the victorious party sustains a certain percentage of their initial resources as losses. This model can serve as a crucial tool for analyzing interactions in complex systems and supporting strategic decision-making .