Multiple μ-stability and multiperiodicity of delayed memristor-based fuzzy cellular neural networks with nonmonotonic activation functions

In this paper, the multistability and multiperiodicity problems are investigated for the memristor-based fuzzy cellular neural networks (MFCNNs) with nonmonotonic activation functions and unbounded time-varying delays. Based on the fixed point theorem and the geometrical properties of activation functions, sufficient criteria are obtained to ensure such n-neuron MFCNNs can have at least Pi(n)(i=1)( 2K(i) + 1) equilibrium points with K-i > 0 in which Pi(n)(i=1)(K-i + 1) are locally mu-stable. As an extension of the theory, the existence of Pi(n)(i=1)(K-i + 1) locally exponentially stable periodic solutions with time-periodic inputs is also derived. Finally, one example is presented to confirm our results. (C) 2018 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.