Multiple μ-stability analysis for memristor-based complex-valued neural networks with nonmonotonic piecewise nonlinear activation functions and unbounded time-varying delays

This paper concentrates on the coexistence and dynamical behaviors of multiple equilibrium points for a class of memristor-based complex-valued neural networks (MCVNNs) with non-monotonic piecewise nonlinear activation functions and unbounded time-varying delays. Based on the geometrical configuration of activation functions, by utilizing the Intermediate Value Theorem and other analytical tools, some novel algebraic criteria are proposed to guarantee the coexistence of 25 n equilibrium points in which 9 n equilibrium points are locally mu-stable for such MCVNNs. As a direct application of these results, some criteria that assure the multiple exponential stability, multiple power stability, multiple log-stability and multiple log-log-stability are established. The proposed results show that the complex-valued neural networks introduced in this paper can have greater storage capacity than the real-valued ones. Finally, numerical example is presented to demonstrate the validity and feasibility of the obtained theoretical findings. (C) 2017 Elsevier B.V. All rights reserved.