On the complete synchronization of a time-fractional reaction-diffusion system with the Newton-Leipnik nonlinearity

TL;DR

This paper investigates the synchronization of a time-fractional reaction-diffusion system with Newton-Leipnik nonlinearity, providing stability conditions, chaos analysis, and a nonlinear controller for synchronization.

Contribution

It introduces a novel fractional reaction-diffusion model with Newton-Leipnik nonlinearity and develops a synchronization controller with proven stability.

Findings

Derived sufficient conditions for asymptotic stability.

Established the existence of chaos in the system.

Designed a nonlinear synchronization controller with proven convergence.

Abstract

In this paper, we consider a time-fractional reaction-diffusion system with the same nonlinearities of the Newton-Leipnik chaotic system. Through analytical tools and numerical results, we derive sufficient conditions for the asymptotic stability of the proposed model and show the existence of chaos. We also propose a nonlinear synchronization controller for a pair of systems and establish the local and global asymptotic convergence of the trajectories by means of fractional stability theory and the Lyapunov method.