Forward and Pullback Dynamics of Nonautonomous Integrodifference Equations: Basic Constructions

TL;DR

This paper develops a theoretical framework for analyzing the long-term dynamics of nonautonomous integrodifference equations, which model species dispersal in environments with aperiodic influences, by constructing pullback and forward attractors.

Contribution

It introduces a novel approach to understanding the future behavior of nonautonomous integrodifference equations through the construction of attractors and limit sets.

Findings

Constructed pullback and forward attractors for nonautonomous integrodifference equations.

Provided a comprehensive analysis of long-term behavior in infinite-dimensional systems.

Extended the theory of attractors to applications in ecological models with environmental variability.

Abstract

In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an aperiodic influence on the models leading to nonautonomous integrodifference equations. In order to capture their long-term behaviour comprehensively, both pullback and forward attractors, as well as forward limit sets are constructed for general infinite-dimensional nonautonomous dynamical systems in discrete time. While the theory of pullback attractors, but not their application to integrodifference equations, is meanwhile well-established, the present novel approach is needed in order to understand their future behaviour.