Global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays

The paper presents theoretical results on the global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays. The dynamic analysis in the paper employs the theory of differential equations with discontinuous right-hand side as introduced by Filippov. By using the inequality techniques and a useful Lyapunov functional, some new testable algebraic criteria are obtained for ensuring the existence and global exponential stability of periodic solution of the system. The model based on the memristor widens the application scope for the design of neural networks, and the new effective results also enrich the toolbox for the qualitative analysis of neural networks.