Multistability analysis of switched fractional-order recurrent neural networks with time-varying delay

This paper focuses on the existence and dynamic behaviors of multiple equilibria of switched fractional-order recurrent neural networks (SFRNNs) with time-varying delay. By applying the characteristics of Caputo fractional calculus and an effective state space partition method, sufficient criteria are derived to ascertain that the n-neuron SFRNN has 5n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$5^n$$\end{document} equilibria, among which 3n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3^n$$\end{document} ones are locally asymptotically stable and the rest are unstable. Moreover, the multistability of integer-order neural networks as a special case is also taken into consideration in this paper. Two illustrative examples are provided to substantiate the theoretical results.