A model for dynamical systems with strange attractors

TL;DR

This paper introduces a simplified one-degree-of-freedom model for chaotic dynamical systems with strange attractors, using a second-order integro-differential equation that exhibits self-oscillation and mimics spring-like behavior.

Contribution

It presents a novel reduced-order model capturing key features of strange attractors in three-dimensional systems, including energy characteristics and self-oscillation.

Findings

Model accurately reproduces chaotic attractor characteristics

System exhibits self-oscillation behavior

Potential energy and kinetic energy dynamics are characterized

Abstract

We derive a system with one degree of freedom that models a class of dynamical systems with strange attractors in three dimensions. This system retains all the characteristics of chaotic attractors and is expressed by a second-order integro-differential equation which mimics a spring-like problem. We determine the potential energy, the rate of change of the kinetic energy of this system, and show that is self-oscillating.