Abstract: Based on two fractional-order chaotic complex drive systems and one fractional-order chaotic complex response system with different dimensions, we propose generalized combination complex synchronization. In this new synchronization scheme, there are two complex scaling matrices that are non-square matrices. On the basis of the stability theory of fractional-order linear systems, we de...

In this paper, synchronization of two chaotic signals is studied and analyzed. A nonlinear recursive backstepping scheme is utilized to design an appropriate control input signal that achieves synchronization between the two chaotic signals. For the sake of comparison, an alternative master-slave synchronizing controller is designed and the two controllers are compared. Numerical simulations ar...

Aiming at the abrupt faults of the chaotic system, an adaptive observer is proposed to trace the states of the master system. The sufficient conditions for synchronization of such chaotic systems are also derived. Then the feasibility and effectiveness of the proposed method are illustrated via numerical simulations of chaotic Chen system. Finally, the proposed synchronization schemes are appli...

This paper investigates the adaptive chaos control and synchronization of the Shaw chaotic system (Shaw, 1981) with unknown parameters. First, we design adaptive control laws to stabilize the Shaw chaotic system with unknown parameters to its unstable equilibrium at the origin based on the adaptive control theory and Lyapunov stability theory. Next, we derive adaptive control laws to achieve gl...

in this paper, we discuss the dynamical properties of a chemical reactor model including lyapunov exponents, bifurcation, stability of equilibrium and chaotic attractors as well as necessary conditions for this system to generate chaos. we study the synchronization of chemical reactors model via sliding mode control scheme. the stability of proposed method is proved by barbalate’s lemma. numeri...

Experimental results are presented on the effect of coupling on synchronization of two coupled nonidentical Chua’s oscillators. Two oscillators are coupled in unidirectional drive response mode. The driver is always kept in chaotic ~single scroll, double scroll! state while the response oscillator is kept in various dynamical states as point attractor, single scroll periodic, chaotic and double...

In this paper, a new general chaos synchronization scheme is proposed for coupled arbitrary 3-D quadratic chaotic dynamical systems in discrete-time. The proposed synchronization method, based on nonlinear controllers and Lyapunov stability theory, is theoretically rigorous. The derived synchronization criterion can be also applicable to a large class of discrete-time chaotic systems. Our contr...

In this paper, a projective synchronization approach for a class of fractional-order chaotic systems with fractional-order 1 < q < 2 is demonstrated. The projective synchronization approach is established through precise theorization. To illustrate the effectiveness of the proposed scheme, we discuss two examples: (1) the fractional-order Lorenz chaotic system with fractional-order q = 1.1; (2)...

The chaotic synchronization of third-order systems and second-order driven oscillator is studied in this paper. Such a problem is related to synchronization of strictly different chaotic systems. We show that dynamical evolution of second-order driven oscillators can be synchronized with the canonical projection of a third-order chaotic system. In this sense, it is said that synchronization is ...

In this paper, we discuss the dynamical properties of a chemical reactor model including Lyapunov exponents, bifurcation, stability of equilibrium and chaotic attractors as well as necessary conditions for this system to generate chaos. We study the synchronization of chemical reactors model via sliding mode control scheme. The stability of proposed method is proved by Barbalate’s lemma. Numeri...