Pullback and forward attractors of contractive difference equations

TL;DR

This paper demonstrates that under contractivity assumptions, the attractors of dissipative difference equations are unique and coincide for pullback and forward cases, simplifying their structure and application in ecological models.

Contribution

It introduces contractivity conditions replacing compactness assumptions to establish the equivalence of pullback and forward attractors, leading to unique bounded solutions.

Findings

Pullback and forward attractors are identical under contractivity.

Attractors degenerate to unique bounded entire solutions.

Application to ecological integrodifference equations.

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.