Multistability of complex-valued neural networks with time-varying delays

In this paper, the multistability problem is studied for an n-dimensional delayed complex-valued neural networks with two general classes of activation functions. After splitting the state space to multiple subsets, based on the fixed point theorem, it is shown that such complex-valued neural networks can have 9n equilibria, each of which is located in one of the subsets. Furthermore, some sufficient conditions are derived for the local exponential stability of some equilibria by employing the property of activation functions and inequality technique. As an application of these results, some criteria are obtained for checking the coexistence and exponential stability of multiple equilibria of real-valued neural networks. Two examples are performed to illustrate and validate the theoretical findings.