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

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.

COMMUNICATED BY:

• Brahim Amaziane

Keywords:

• Newton–Leipnik
• fractional chaotic system
• reaction diffusion
• chaos synchronization
• complete synchronization

AMS CLASSIFICATIONS:

• 34A08
• 34H10
• 34D06

Disclosure statement

No potential conflict of interest was reported by the authors.