Adaptive synchronization of fractional-order memristor-based neural networks with multiple time-varying delays

This paper is concerned with globally asymptotical synchronization of fractional-order memristor-based neural networks (FMNNs) with multiple time-varying delays. Based on the definition of memristors, a more practical model of FMNNs with multiple time-varying delays is constructed from the integerorder counterparts. FMNNs are represented by fractional-order differential equations with discontinuous right-hand sides, which makes traditional definition of solutions for fractional-order differential equations inapplicable to FMNNs. This problem is handled with the theory of Filippov solutions. By combining state feedback control with adaptive control, a novel and simple adaptive feedback controller is designed to make two FMNNs achieve globally asymptotical synchronization. By constructing a suitable Lyapunov function, globally asymptotical stability of the controlled synchronization error system can be guaranteed theoretically. Finally, a numerical example is given to illustrate the effectiveness of the designed controller.

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