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MiS Preprint
7/2011

Local attractor continuation of non-autonomously perturbed systems

Martin Kell

Abstract

Using Conley theory we show that local attractors remain (past) attractors under small non-autonomous perturbations. In particular, the attractors of the perturbed systems will have positive invariant neighborhoods and converge upper semicontinuously to the original attractor.

The result is split into a finite-dimensional part (locally compact) and an infinite-dimensional part (not necessarily locally compact). The finite-dimensional part will be applicable to bounded random noise, i.e. continuous time random dynamical systems on a locally compact metric space which are uniformly close the unperturbed deterministic system. The “closeness” will be defined via a (simpler version of) convergence coming from singular perturbations theory.

Received:
Mar 17, 2011
Published:
Mar 21, 2011
MSC Codes:
37B55, 37B35, 37L15
Keywords:
local attractor, non-autonomous perturbation, bounded noise

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2011 Repository Open Access
Martin Kell

Local attractor continuation of non-autonomously perturbed systems