Multistability of Recurrent Neural Networks With Piecewise-Linear Radial Basis Functions and State-Dependent Switching Parameters

Abstract

This paper presents new theoretical results on the multistability of switched recurrent neural networks with radial basis functions and state-dependent switching. By partitioning state space, applying Brouwer fixed-point theorem and constructing a Lyapunov function, the number of the equilibria and their locations are estimated and their stability/instability are analyzed under some reasonable assumptions on the decomposition of index set and switching threshold. It is shown that the switching threshold plays an important role in increasing the number of stable equilibria and different multistability results can be obtained under different ranges of switching threshold. The results suggest that switched recurrent neural networks would be superior to conventional ones in terms of increased storage capacity when used as associative memories. Two examples are discussed in detail to substantiate the effectiveness of the theoretical analysis.