Title: Chaos and synchronisation of a new fractional order system with only two stable equilibria

Authors: Yuhan Zhao; Ranchao Wu

Addresses: School of Mathematics, Anhui University, Hefei, Anhui, China ' School of Mathematics, Anhui University, Hefei, Anhui, China

Abstract: In this paper, a new fractional order three-dimensional autonomous quadratic generalised Sprott C chaotic system is proposed. It is found that it has only two stable equilibria. That means that it is different from general fraction order chaotic systems, which often have unstable equilibrium points. First, some sufficient conditions for local stability of equilibria are given. Note that in the parameter space where the equilibria of the system are both asymptotically stable, it is confirmed by numerical simulation that chaotic attractors coexist with two stable equilibria. Then synchronisation between such systems is analysed. Unlike the active control scheme, which will cause the error system to be linear, here the error system is still kept to be non-linear. By Lyapunov stability theory, synchronisation is realised. Numerical simulation is performed to verify the theoretical results.

Keywords: chaos; fractional order systems; synchronisation; stable equilibria; Sprott C chaotic systems; numerical simulation; chaotic attractors; Lyapunov stability theory.

DOI: 10.1504/IJDSDE.2016.079024

International Journal of Dynamical Systems and Differential Equations, 2016 Vol.6 No.3, pp.187 - 202

Received: 11 Apr 2015
Accepted: 21 Dec 2015
Published online: 09 Sep 2016 *

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