Dynamical behavior of impulsive and periodic Cohen–Grossberg neural networks

This paper investigates the existence and global stability of the periodic solution x∘(t) to Cohen–Grossberg neural networks with periodic coefficients and impulses. By using comparison results for impulsive differential equations and the method of Lyapunov, we describe the asymptotic behavior of all solutions. In addition, we give an explicit formula for the rate of exponential decay at infinity of the Euclidean norm ‖x(t)−x∘(t)‖, where x(t)x(t) is any solution of our model. Such a formula involves the jumps and the average of a suitable periodic function depending on the other parameters of the neural networks.