Complete synchronization of the Newton--Leipnik reaction diffusion chaotic system

TL;DR

This paper develops a nonlinear synchronization scheme for a reaction-diffusion version of the Newton-Leipnik chaotic system, proving its stability both locally and globally, with numerical validation.

Contribution

It introduces a novel synchronization method for the reaction-diffusion Newton-Leipnik system and demonstrates its stability analytically and numerically.

Findings

Successful global stability proof using Lyapunov functional

Numerical example confirming theoretical results

Effective synchronization of the chaotic reaction-diffusion system

Abstract

In this paper we investigate the reaction--diffusion system corresponding to the Newton--Leipnik chaotic system originally developed to model the rigid body motion through linear feedback (LFRBM). We develop a nonlinear synchronization scheme for the proposed reaction--diffusion system and prove its global stability in the local sense by means of the eigenvalues of the Jacobian and global sense through an appropriate Lyapunov functional. A numerical example is presented to illustrate the results of this study.