In this paper, we focus on the synchronization between integer-order chaotic systems and a class of fractional-order chaotic system using the stability theory of fractional-order systems. A new fuzzy sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions. Furthermore, three examples are presented to illustrate the effectiveness of the pr...

Keywords: Lorenz-like systems Lorenz system Chen system Lu system Lyapunov exponent Chaotic analog of 16th Hilbert problem a b s t r a c t Currently it is being actively discussed the question of the equivalence of various Lorenz-like systems and the possibility of universal consideration of their behavior (in view of the possibility of reduction of such systems to the same form with the help o...

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 study demonstrates the modified projective synchronization in Chen-Lee chaotic system. The variable structure control technology is used to design the synchronization controller with input nonlinearity. Based on Lyapunov stability theory, a nonlinear controller and some generic sufficient conditions can be obtained to guarantee the modified projective synchronization, including synchroniza...

Abstract. This paper discusses chaos synchronization between two identical or different fractional order chaotic systems. Base on linear matrix inequality, two new synchronization criterions are constructed by which it is proved that two identical (Lü system) or different (Lü and Chen systems) fractional order chaotic systems are synchronized using the simple linear feedback control laws. Final...

This paper investigates the functional projective synchronization problem for chaotic systems. Based on Lyapunov stability theory, a nonlinear control scheme for the synchronization is proposed. Numerical simulations on Chen chaotic system are presented to verify the usefulness of the proposed control scheme.

This chapter proposes and studies a memristor-based chaotic system, which is constructed by incorporating a memristor into the canonical Chen oscillator with boundary conditions. Specifically, charge-controlled and flux-controlled memristor models with appropriate boundary conditions are introduced and the relation between the charge through and the flux across the memristor is derived. The ric...

In this paper, it is considered that chaos synchronization of Chen fractional order time-delay chaotic systems and its application in secure communication. By use of the fractional calculus techniques, we find that chaos exists in the fractional order Chen system with time delays when the order is less than 3. Firstly, based on the Laplace transform theory, the conditions for achieving synchron...

This paper investigates the reconstruction problem for the Lorenz and Chen systems using noisy observation data. Both theoretical and numerical results show that the relatively accurate reconstruction of these two chaotic systems can be obtained under the condition of small random disturbance to the observations. These results also show that the model reconstruction accuracy can be enhanced by ...