Multistability of state-dependent switching neural networks with discontinuous nonmonotonic piecewise linear activation functions

Abstract This paper presents the theoretical results on the multistability of state-dependent switching neural networks with discontinuous nonmonotonic piecewise linear activation functions. For n-neurons switching model, this paper shows that neural networks have 7n equilibrium points, 6n of which are located at the continuous points of activation functions and others are located at the discontinuous points of activation functions. Among these equilibrium points, 4n or 5n are stable and others are unstable, which depend on the relationship between the switching threshold and the discontinuous points of the activation functions. Compared with existing results, this paper reveals that switching threshold and discontinuous character are crucial in increasing the number of equilibrium points. Two examples are presented to verify the theoretical results.