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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.

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