含快变时滞的格FitzHugh-Nagumo系统的拉回吸引子

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

摘要:

本文研究具有快时滞影响的格FitzHugh-Nagumo方程的动力学行为，证明了拉回吸引子的存在和唯一性. 一般来说,研究时滞方程吸引子要求时滞项的导数小于1（慢时滞）, 本文则使用差分不等式技巧消除了这个约束. 因而本文的结果可被用于处理具有快变延迟的方程.

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.