期刊
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
卷 32, 期 1, 页码 229-240出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2020.2978267
关键词
Recurrent neural networks; Stability criteria; Asymptotic stability; Delay effects; Numerical stability; Countably infinite number of equilibria; recurrent neural networks; sinusoidal activation function; stability
类别
资金
- National Natural Science Foundation of China [61673330, 61703313]
- Research Grants Council of the Hong Kong Special Administrative Region, China [11208517, 11202318]
- International Partnership Program of Chinese Academy of Sciences [GJHZ1849]
- Natural Science Foundation of Hunan [2019JJ40022]
This article presents new theoretical results on multistability and complete stability of recurrent neural networks with a sinusoidal activation function, including sufficient criteria for stability and estimation of attraction basins. In contrast to existing results, the new criteria are applicable for both finite and countably infinite numbers of equilibria.
This article presents new theoretical results on multistability and complete stability of recurrent neural networks with a sinusoidal activation function. Sufficient criteria are provided for ascertaining the stability of recurrent neural networks with various numbers of equilibria, such as a unique equilibrium, finite, and countably infinite numbers of equilibria. Multiple exponential stability criteria of equilibria are derived, and the attraction basins of equilibria are estimated. Furthermore, criteria for complete stability and instability of equilibria are derived for recurrent neural networks without time delay. In contrast to the existing stability results with a finite number of equilibria, the new criteria, herein, are applicable for both finite and countably infinite numbers of equilibria. Two illustrative examples with finite and countably infinite numbers of equilibria are elaborated to substantiate the results.
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