Pullback attractors for lattice FitzHugh-Nagumo systems with fast-varying delays

Abstract:

We investigate the dynamical behavior of lattice FitzHugh-Nagumo equation with fast-varying delays and obtain the existence and uniqueness of pullback attractor for the equation. Generally, studying the attractors of a time-varying delay equation require that the derivative of the delay term is less than 1 ( slow-varying delay). However, in this paper, by using some differential inequality techniques we remove this constraint. Therefore, our method can be used to deal with the equations with fast-varying delays.