Existence and global exponential stability of periodic solution of cellular neural networks with delay and impulses (Q708735)

This work investigates a system of differential equations modeling a neural network, including time-delays, periodic forcing, and also impulses to the system delivered at a periodic intervals. The aim is to study the periodic solution for this system, with period identical to that of the impulses. A theorem ensuring the existence is proved, using Mawhin's continuation theorem. Under certain restrictions on the nonlinearity and the strength of the impulses, the global exponential asymptotic stability of the periodic solution is proved, employing a Lyapunov-Krasovsky functional.