Multistability of recurrent neural networks with general periodic activation functions and unbounded time-varying delays

This paper investigates the multistability of recurrent neural networks (RNNs) with unbounded time-varying delays whose activation functions are general periodic functions. The activation function can be linear, nonlinear, or have multiple corner points, as long as it satisfies Lipschitz continuous condition. According to the characteristics of the parameters of the RNNs and the state space division method, the number of equilibrium points (EPs) of the RNNs is split into three categories, which can be unique, finite, or countable infinite. Some sufficient conditions for determining the number of EPs are presented, the criterion of asymptotically stable EPs is deduced, and the attraction basins of stable EPs are estimated. Furthermore, the multistability results in this paper are an extension of some previous results. The theoretical results are validated using three numerical simulation examples.