Multimode function multistability for Cohen-Grossberg neural networks with mixed time delays. (October 2022)

• Record Type: Journal Article
• Authors: Wan, Liguang; Liu, Zhenxing
• Is Part Of: ISA transactions. Volume 129(2022)Part A
• Page Start: 179
• Page End: 192
• Publication Date: 2022-10
• Subjects: Cohen-Grossberg neural networks -- Multimode function stability -- Multistability -- Mixed time delays; Engineering instruments -- Periodicals; Engineering instruments; Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.isatra.2021.11.046
• Languages: English
• ISSNs: 0019-0578

Abstract

Abstract: In this paper, we are concerned with the multimode function multistability for Cohen-Grossberg neural networks (CGNNs) with mixed time delays. It is introduced the multimode function multistability as well as its specific mathematical expression, which is a generalization of multiple exponential stability, multiple polynomial stability, multiple logarithmic stability, and asymptotic stability. Also, according to the neural network (NN) model and the maximum and minimum values of activation functions, n pairs of upper and lower boundary functions are obtained. Via the locations of the zeros of the n pairs of upper and lower boundary functions, the state space is divided into ∏ i = 1 n ( 2 H i + 1 ) parts correspondingly. By virtue of the reduction to absurdity, continuity of function, Brouwer's fixed point theorem and Lyapunov stability theorem, the criteria for multimode function multistability are acquired. Multiple types of multistability, including multiple exponential stability, multiple polynomial stability, multiple logarithmic stability, and multiple asymptotic stability, can be achieved by selecting different types of function P ( t ) . Two numerical examples are offered to substantiate the generality of the obtained criteria over the existing results. Highlights: The concept of multimode function multistability is established for (Cohen-Grossberg neural networks) CGNNs with mixed time delays. Sufficient conditions are obtained to guarantee the existence of ∏ i = 1 n ( H i + 1 ) multimode function stable equilibria for CGNNs with mixed time delays. The obtained results include both multimode function monostability and multimode function multistability for CGNNs with mixed time delays. Invariant sets of the locally multimode function stable equilibria are estimated for CGNNs with mixed time delays, which uncovers the real invariant sets may be larger than the previously partitioned invariant sets.