Multistability analysis of state-dependent switched Hopfield neural networks with the Gaussian-wavelet-type activation function

In multistability analysis, the Gaussian-wavelet-type activation function is shown to have better properties by comparison with sigmoidal functions, saturated functions and Mexican-hat-type functions. State-dependent switched Hopfield neural network (SSHNN) is expected to display even richer dynamical behaviors in contrast with conventional Hopfield neural networks (HNNs). Considering these two reasons, this paper studies the multistability of SSHNNs with the Gaussian-wavelet-type activation function. Some sufficient conditions for the coexistence as well as the stability of multiple equilibria of SSHNNs are derived. It is obtained that SSHNNs with the Gaussian-wavelet-type activation function can have at least 7n or 6n equilibria, of which 4n or 5n are locally stable (LS). We find that, compared with conventional HNNs with the Gaussian-wavelet-type activation function or SSHNNs with other kinds of activation functions, SSHNNs with the Gaussian-wavelet-type activation functions can have more LS equilibria. It implies that SSHNNs with the Gaussian-wavelet-type activation functions have even larger storage capacity and have overwhelming superiority in associative memory applications. Lastly, some simulation results are given to verify the correctness of the theoretical results. (C) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

This study investigates the multistability of SSHNNs with the Gaussian-wavelet-type activation function and finds that it has more locally stable equilibria, increasing storage capacity and advantages in associative memory applications.