Multiple μ-stability analysis of complex-valued neural networks with unbounded time-varying delays

In this paper, we are considered complex-valued neural networks (CVNNs) with unbounded time-varying delays and the problem of multiple μ-stability of the proposed CVNNs is extensively investigated. The choice of activation function is the main challenge in the analysis of CVNNs. Therefore, we chosen the real-imaginary-type activation function for the considered CVNNs. Some new sufficient conditions are derived to ensure that existence of [(2α+1)(2β+1)]n(α,β≥1)[(2α+1)(2β+1)]n(α,β≥1) equilibrium points in which [(α+1)(β+1)]n[(α+1)(β+1)]n equilibrium points are locally μ-stable and the remaining equilibrium points [(2α+1)(2β+1)]n−[(α+1)(β+1)]n[(2α+1)(2β+1)]n−[(α+1)(β+1)]n are unstable for the considered CVNNs. Based on our main results, we can derive some stability conditions such as multiple exponential stability, multiple power stability, multiple log-stability and multiple log–log-stability. Finally, numerical example is presented to show the effectiveness of our theoretical results.