Abstract
This paper investigates the issue of multistability in state-dependent switched neural networks (SSNNs) with Mexican-hat-type activation functions (AFs). It establishes the coexistence and stability of multiple equilibrium points (EPs). Initially, the state space is partitioned based on the geometric characteristics of the Mexican-hat-type AF, enabling to determine the positions of the EPs. Secondly, the coexistence of 9h17h25h33h4 EPs for n-neurons SSNNs under specific sufficient conditions is proved with the Brouwer’s fixed-point theorem. Next, by using diagonally dominant matrix theory and Gershgorin circle theorem, it is proven that there are 5h14h23h32h4 asymptotically stable EPs under some conditions, where h1,h2,h3 and h4 are nonnegative integers satisfying 0≤h1+h2+h3+h4≤n. Therefore, we can obtain that SSNNs can have larger storage capacity by selecting the appropriate parameters hi,i=1,2,3,4. Finally, the correctness of the results in this paper is verified through two numerical examples.
Published Version
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