Almost periodic solution of impulsive Hopfield neural networks with finite distributed delays

Abstract

By the definition of piecewise almost periodic functions, this paper investigates the existence and stability of a discontinuous almost periodic solution of the impulsive Hopfield neural networks with finite distributed delays and periodic impulses, using fixed point theorems, Lyapunov functional, and some inequality techniques. Compared with known relevant results mainly concentrating on continuous neural networks, the obtained criteria consider impulse effects. Moreover, it does not use Cauchy matrix, and the corresponding hypotheses about linear impulse systems which are often used in the reference. The obtained criteria are easily applicable and checkable, and an illustrative example with simulations shows this. Furthermore, the proposed results are applicable to some other networks with periodic impulses.