Analysis of the Structure of Chaotic Solutions of Differential Equations

Abstract

This study deals with the relevant and important area of many fields of mathematics and physics - chaotic systems. Three modified systems of Chua differential equations were considered, and the chaotic structure of their solutions was compared with the structure of solutions of classical Lorentz and Rössler chaotic systems. The following methods were used to achieve the set goal: the Runge-Kutta method, building a phase portrait, determining Lyapunov exponents and noise level, and comparative analysis. A detailed analysis of the structure of chaotic solutions of various differential equations was carried out. It was established that the chaotic solution’s structure depends on the differential equation’s properties and the initial conditions. According to the obtained results, one of the modifications of the Chua system is significantly superior to classical chaotic systems and can be used as a chaos generator. Prospects for further research involve expanding the scope of the study and the generalization of the obtained results for a wider class of systems of differential equations.