Title: Pullback and forward attractors of contractive difference equations

Authors: Huy Huynh; Abdullah Kalkan

Addresses: Institut für Mathematik, Universität Klagenfurt, 9020, Klagenfurt am Wörthersee, Austria ' Institut für Mathematik, Universität Klagenfurt, 9020, Klagenfurt am Wörthersee, Austria

Abstract: The construction of attractors of a dissipative difference equation is usually based on compactness assumptions. In this paper, we replace them with contractivity assumptions under which the pullback and forward attractors are identical. As a consequence, attractors degenerate to unique bounded entire solutions. As an application, we investigate attractors of integrodifference equations which are popular models in theoretical ecology.

Keywords: pullback attractor; forward attractor; contractive mapping; dissipative difference equation; semilinear difference equation; contractive difference equation; integrodifference equation.

DOI: 10.1504/IJDSDE.2021.117363

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.3/4, pp.302 - 321

Received: 29 Jun 2020
Accepted: 22 Nov 2020
Published online: 01 Sep 2021 *

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