Abstract
In this paper, we consider a class of nonautonomous discrete p-Laplacian complex Ginzburg–Landau equations with time-varying delays. We prove the existence and uniqueness of pullback attractor for these equations. The existing results of studying attractors for time-varying delay equations require that the derivative of the delay term should be less than 1 (called slow-varying delay). By using differential inequality technique, our results remove the constraints on the delay derivative. So, we can deal with the equations with fast-varying delays (without any constraints on the delay derivative).
Highlights
Due to numerous applications in physics, biology, and engineering such as pattern formation, propagation of nerve pulses, electric circuits, and so on, see, e.g., [2, 6, 7, 10, 12], lattice differential equations have become a large and growing interdisciplinary area of research
For an understanding of the dynamical behavior of dissipative infinite lattice systems, attractors are especially important because they retain most of the dynamical information
The existence of global attractors for lattice systems was initialed by Bates et al [1], followed by extensions in [3, 8, 13, 16, 19, 24] and the references therein
Summary
Due to numerous applications in physics, biology, and engineering such as pattern formation, propagation of nerve pulses, electric circuits, and so on, see, e.g., [2, 6, 7, 10, 12], lattice differential equations have become a large and growing interdisciplinary area of research. We prove the existence and uniqueness of pullback attractor for these equations. We prove the existence and uniqueness of a pullback attractor for the nonautonomous equations in Sect.
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