A non-autonomous flow system with Plykin type attractor

TL;DR

This paper introduces a non-autonomous flow system with a Plykin type attractor, demonstrating structurally stable chaotic dynamics through a novel geometric transformation-based model and its differential equation representation.

Contribution

It presents a new non-autonomous flow system with a Plykin attractor, including a differential equation model ensuring structural stability and chaotic behavior.

Findings

The system exhibits a Plykin type attractor in simulations.

The attractor is structurally stable across parameter ranges.

The model can be represented on a plane via stereographic projection.

Abstract

A non-autonomous flow system is introduced with an attractor of Plykin type that may serve as a base for elaboration of real systems and devices demonstrating the structurally stable chaotic dynamics. The starting point is a map on a two-dimensional sphere, consisting of four stages of continuous geometrically evident transformations. The computations indicate that in a certain parameter range the map has a uniformly hyperbolic attractor. It may be represented on a plane by means of a stereographic projection. Accounting structural stability, a modification of the model is undertaken to obtain a set of two non-autonomous differential equations of the first order with smooth coefficients. As follows from computations, it has the Plykin type attractor in the Poincar\'{e} cross-section.