Numerical Dynamics of Integrodifference Equations: Forward Dynamics and Pullback Attractors

TL;DR

This paper develops criteria for the existence and stability of forward and pullback attractors in nonautonomous difference equations, with applications to spatially discretized integrodifference equations.

Contribution

It provides new theoretical conditions for attractor existence and stability in nonautonomous systems, including perturbation persistence and convergence results.

Findings

Criteria for existence of attractors in nonautonomous difference equations

Persistence of attractors under perturbations

Application to spatial discretization of integrodifference equations

Abstract

In order to determine the dynamics of nonautonomous equations both their forward and pullback behavior need to be understood. For this reason we provide sufficient criteria for the existence of such attracting invariant sets in a general setting of nonautonomous difference equations in metric spaces. In addition it is shown that both forward and pullback attractors, as well as forward limit sets persist and that the latter two notions even converge under perturbation. As concrete application, we study integrodifference equation under spatial discretization of collocation type.