Class Of Fractional-order Chaotic Systems Research Articles

Adaptive synchronization of the fractional-order unified chaotic system

This article proposes an adaptive synchronization method with only one controller for the fractional-order unified chaotic system, and adaptive controller and updating law of parameter are obtained. The controller employs a single variable, and the presented control scheme is suitable for a class of fractional-order chaotic systems. In addition, the synchronization is effective in the presence of noise. Numerical simulations are used to validate and demonstrate the effectiveness of the proposed method.

Generalized projective synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal

In this Letter, a drive-response synchronization method with linear output error feedback is presented for “generalized projective synchronization” of a class of fractional-order chaotic systems via a scalar transmitted signal. This synchronization approach is theoretically and numerically studied. By using stability theory of linear fractional-order systems, the suitable conditions for achieving synchronization are given. Two examples are used to illustrate the effectiveness of the proposed synchronization method. Numerical simulations coincide with the theoretical analysis.

Nonlinear observer based full-state projective synchronization for a class of fractional-order chaotic system

In this paper, based on the stability theory of the fractional-order system, an idea of using state observer to realize the full-state projective synchronization of fractional-order chaotic system is proposed. The designed observer can achieve full-state projective synchronization in a class of nonlinear fractional-order systems without the limitation of partial-linearity, extend the scope of application of projective synchronization, and does not require the calculation of the conditional Lyapunov exponents. In addition, this synchronization method is simple and theoretically rigorous, capable to achieve a full-state synchronization of arbitrary scaling factor. Finally, the method has been applied to realize the full-state projective synchronization of fractional-order Rssle system, and the simulation results verified the effectiveness of the method.

Chaotic synchronization for a class of fractional-order chaotic systems

In this paper, a very simple synchronization method is presented for a class of fractional-order chaotic systems only via feedback control. The synchronization technique, based on the stability theory of fractional-order systems, is simple and theoretically rigorous.

Nonlinear observer design to synchronize fractional-order chaotic systems via a scalar transmitted signal

In this paper, based on the idea of nonlinear observer and stability theory of fractional-order systems, a new systematic scheme to synchronize a class of fractional-order chaotic systems via a scalar transmitted signal is developed. The approach is simple, global and theoretically rigorous. It enables synchronization of fractional-order chaotic systems to be achieved in a systematic way and does not require the computation of the conditional Lyapunov exponents. Simulation results are used to visualize and illustrate the effectiveness of the proposed synchronization method.

Synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal

Abstract In this paper, a drive-response synchronization method with linear output error feedback is presented for synchronizing a class of fractional-order chaotic systems via a scalar transmitted signal. Based on stability theory of fractional-order systems and linear system theory, a necessary and sufficient condition for the existence of the feedback gain vector such that global synchronization between the fractional-order drive system and response system can be achieved and its design method are given. This synchronization approach that is simple, global and theoretically rigorous enables synchronization of fractional-order chaotic systems be achieved in a systematic way and does not require the computation of the conditional Lyapunov exponents. An example is used to illustrate the effectiveness of the proposed synchronization method.