Invariant measures for first order nonlocal lattice dynamical systems with delays

Abstract

In this article, we study the first order nonlocal lattice dynamical systems with variable and distributed delays. Firstly, we establish the global well-posedness of solutions for this lattice system by overcoming difficulties caused by the nonlocal operator and delay terms. Then, we show that the associated process generated by this equation possesses a pullback-Dµ attractor. Finally, we further construct the invariant measures for this nonlocal delayed system on infinite lattices.