期刊
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
卷 32, 期 1, 页码 177-187出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2020.2977994
关键词
Delays; Stability criteria; Biological neural networks; Asymptotic stability; Numerical stability; Attraction; fractional-order neural networks (FONNs); Mittag-Leffler stability; multistability; unbounded time-varying delays
类别
资金
- National Key Research and Development Program of China [2016YFB0800402]
- Natural Science Foundation of China [61906071, 61936004, 61673188]
- China Postdoctoral Science Foundation [2019M652645]
- Innovation Group Project of the National Natural Science Foundation of China [61821003]
- Foundation for Innovative Research Groups of Hubei Province of China [2017CFA005]
- 111 Project on Computational Intelligence and Intelligent Control [B18024]
This article discusses the multistability and attraction of fractional-order neural networks with unbounded time-varying delays. Multiple sufficient conditions are provided for the coexistence of equilibrium points with concave-convex activation functions. The criteria for Mittag-Leffler stability can be simplified to M-matrix and the extension of attraction basin is shown to be independent of the magnitude of delays. Three numerical examples are given to demonstrate the validity of the theoretical results.
This article addresses the multistability and attraction of fractional-order neural networks (FONNs) with unbounded time-varying delays. Several sufficient conditions are given to ensure the coexistence of equilibrium points (EPs) of FONNs with concave-convex activation functions. Moreover, by exploiting the analytical method and the property of the Mittag-Leffler function, it is shown that the multiple Mittag-Leffler stability of delayed FONNs is derived and the obtained criteria do not depend on differentiable time-varying delays. In particular, the criterion of the Mittag-Leffler stability can be simplified to M-matrix. In addition, the estimation of attraction basin of delayed FONNs is studied, which implies that the extension of attraction basin is independent of the magnitude of delays. Finally, three numerical examples are given to show the validity of the theoretical results.
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