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Stability and synchronization of memristor-based fractional-order delayed neural networks. (English) Zbl 1398.34096
Summary: Global asymptotic stability and synchronization of a class of fractional-order memristor-based delayed neural networks are investigated. For such problems in integer-order systems, Lyapunov-Krasovskii functional is usually constructed, whereas similar method has not been well developed for fractional-order nonlinear delayed systems. By employing a comparison theorem for a class of fractional-order linear systems with time delay, sufficient condition for global asymptotic stability of fractional memristor-based delayed neural networks is derived. Then, based on linear error feedback control, the synchronization criterion for such neural networks is also presented. Numerical simulations are given to demonstrate the effectiveness of the theoretical results.

MSC:
34K20 Stability theory of functional-differential equations
34K37 Functional-differential equations with fractional derivatives
34K25 Asymptotic theory of functional-differential equations
34D06 Synchronization of solutions to ordinary differential equations
34A36 Discontinuous ordinary differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
34K35 Control problems for functional-differential equations
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