On a High-Precision Method for Studying Attractors of Dynamical Systems and Systems of Explosive Type

TL;DR

This paper introduces a high-precision numerical method for approximating attractors in chaotic dynamical systems and identifying asymptotes in explosive systems, with applications to models like population explosion and Chua circuits.

Contribution

It presents a novel high-precision numerical approach for studying attractors and asymptotes in complex dynamical systems, extending to piecewise smooth systems.

Findings

Proved a theorem on the existence of asymptotes in explosive systems.

Extended the numerical method to piecewise smooth systems.

Applied the method to models like population explosion and Chua system.

Abstract

The author of this article considers a numerical method that uses high-precision calculations to construct approximations to attractors of dynamical systems of chaotic type with a quadratic right-hand side, as well as to find the vertical asymptotes of solutions of systems of explosive type. A special case of such systems is the population explosion model. A theorem on the existence of asymptotes is proved. The extension of the numerical method for piecewise smooth systems is described using the Chua system as an example, as well as systems with hysteresis.