Well-posedness and dynamics of double time-delayed lattice FitzHugh–Nagumo systems

Abstract

This paper is concerned with the well-posedness and dynamics of FitzHugh–Nagumo systems with variable delay defined on infinite lattices. We first prove the existence and uniqueness of solutions as well as the existence of an evolution process for this system. We then establish the existence of tempered pullback attractors and invariant measures. Finally, we study the upper semicontinuity of pullback attractors as the delay time tends to zero.

Keywords:

• Delay FitzHugh–Nagumo system
• lattice dynamical system
• pullback attractor
• invariant measure
• upper semicontinuity

2020 Mathematics Subject Classifications:

• 35B40
• 35B41
• 37L30
• 37L40

Disclosure statement

No potential conflict of interest was reported by the author(s).