Chaotifiying continuous-time systems by symmetry

TL;DR

This paper introduces a method to create chaotic continuous-time systems with multiple equilibria by adding symmetry, enabling controlled chaos with symmetrical properties.

Contribution

The paper presents a novel symmetry-based approach to generate chaotic systems with multiple equilibria, expanding the toolkit for designing complex dynamical behaviors.

Findings

Method successfully creates systems with desired number of equilibria.

Generated systems exhibit chaos while maintaining symmetrical equilibria.

The approach offers a new way to control and design chaotic dynamics.

Abstract

In this letter we present a method of constructing dynamical systems with any preassigned number of equilibria by adding symmetry to another system with at least one equilibrium point. If the resulting system is chaotic, we call this procedure chaotification by symmetry since the resulting system is chaotic with many symmetrical equilibrium points.