Stability analysis for quaternion-valued inertial memristor-based neural networks with time delays

Abstract

Quaternion-valued inertial memristor-based neural networks with time-varying delays are found to be effective in demonstrating complex dynamic behaviors. Considering the stability of the periodic solution for a novel neural network, we construct a class quaternion-valued inertial memristor-based neural network model by combining with the cellular neural networks and the inertial item with time-varying delay. Based on the continuation theorem of Mawhin’s coincidence degree theory, differential inclusion theory, and inequality techniques, some sufficient criteria for the existence of periodic solutions are obtained. Meanwhile, through constructing a novel Lyapunov functional method, several sufficient conditions have been derived to ensure the global exponential stability of periodic solutions. At last, an example is provided to illustrate the obtained theoretical results of the quaternion-valued inertial memristor-based neural networks model.