Synchronization of a Class of Fractional-Order Chaotic Neural Networks

Abstract

Abstract:The synchronization problem is studied in this paper for a class of fractional-order chaotic neural networks. By using the Mittag-Leffler function, M-matrix and linear feedback control, a sufficient condition is developed ensuring the synchronization of such neural models with the Caputo fractional derivatives. The synchronization condition is easy to verify, implement and only relies on system structure. Furthermore, the theoretical results are applied to a typical fractional-order chaotic Hopfield neural network, and numerical simulation demonstrates the effectiveness and feasibility of the proposed method.

Robust Control of a Class of Uncertain Fractional-Order Chaotic Systems with Input Nonlinearity via an Adaptive Sliding Mode Technique

“…are the gains of adaptation, it is obvious that 0 (14) and controller (27) will converge to the sliding surface 0  s .…”

“…Therefore, the proof is completed. Once a proper sliding surface has been designed, it is followed by designing an adaptive control law to force the state trajectories of system (14) onto the sliding surface and stay on it forever. The control law for the nonlinearities defined in Equations (15) and (16) are given by Equations (27) and (28), respectively:…”

“…It is not difficult to see that all state trajectories converge to zero asymptotically, which implies that a class of uncertain fractional-order chaotic systems (14) with sector nonlinear input can be stabilized. …”

“…On the basis of Theorem 2, if system (14) subject to dead-zone nonlinear input, then we have the following theorem. (14) with unknown bounded uncertainties and dead-zone nonlinear input. Then the closed-loop system consisting of uncertain system (14) and controller (28) will converge to the sliding surface 0  s .…”

“…Lu [13] developed a nonlinear observer to synchronize the chaotic systems. Chen et al [14,15] researched the synchronization of fractional-order chaotic neural networks. With the development of sliding mode control (SMC) technique, SMC approach has became a universal method to realize the stabilization or synchronization of chaotic systems [16][17][18][19][20].…”