Journal
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
Volume 49, Issue 12, Pages 2519-2535Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSMC.2018.2836952
Keywords
Complex-value memristive neural networks; global asymptotical stability; time-varying delays; ultimate Mittag-Leffler synchronization
Funding
- Natural Science Foundation of China [61603129, 61673188, 61761130081]
- National Key Research and Development Program of China [2016YFB0800402]
- Foundation for Innovative Research Groups of Hubei Province of China [2017CFA005]
- Fundamental Research Funds for the Central Universities [2017KFXKJC002]
- Natural Science Foundation of Hubei Province [2016CFC734]
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This paper investigates some dynamic behaviors for a fractional-order complex-valued memristive neural networks (FCVMNNs) with delays. A new mathematical expression of the complex-value memductance (memristance) is proposed according to the feature of the complex-valued memristor-based neural networks and a new class of FCVMNNs with delays is designed. Based on the framework of Filippov solution and differential inclusion theory, the sufficient conditions are given first to guarantee the global uniform asymptotic stability for the new FCVMNNs with delays, by using fractional-order Leibniz rule and a Razumikhin-type method. In addition, a complex-value adaptive controller is designed to achieve ultimate Mittag-Leffler synchronization between two FCVMNNs with delays. Numerical simulations are given to show the effectiveness of the theoretical results.
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