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Finite-time synchronization of fractional-order memristor-based neural networks with time delays. (English) Zbl 1398.34110
Summary: In this paper, we consider the problem of finite-time synchronization of a class of fractional-order memristor-based neural networks (FMNNs) with time delays and investigated it potentially. By using Laplace transform, the generalized Gronwall’s inequality, Mittag-Leffler functions and linear feedback control technique, some new sufficient conditions are derived to ensure the finite-time synchronization of addressing FMNNs with fractional order \(\alpha:1<\alpha<2\) and \(0<\alpha<1\). The results from the theory of fractional-order differential equations with discontinuous right-hand sides are used to investigate the problem under consideration. The derived results are extended to some previous related works on memristor-based neural networks. Finally, three numerical examples are presented to show the effectiveness of our proposed theoretical results.

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