On the periodic dynamics of memristor-based neural networks with time-varying delays

Abstract

In this paper, we study the existence, uniqueness and stability of periodic solution for a wide class of memristor-based neural networks with time-varying delays. By employing the topological degree theory in set-valued analysis, differential inclusions theory and a new Lyapunov function method, we prove that the neural network has a unique periodic solution, which is globally exponentially stable. Moreover, we prove the existence, uniqueness and global exponential stability of equilibrium point for time-varying delayed memristor-based neural networks with constant coefficients. The obtained results improve and extend previous works on memristor-based or usual neural network dynamical systems with continuous or discontinuous right-hand side. Finally, two numerical examples are provided to show the applicability and effectiveness of our main results.