May  2003, 9(3): 727-744. doi: 10.3934/dcds.2003.9.727

Attractors for nonautonomous and random dynamical systems perturbed by impulses

1. 

Department of Sciences,, University of Applied Sciences, Geusaer Strasse, 06217 Merseburg, Germany

Received  December 2001 Revised  November 2002 Published  February 2003

Nonautonomous and random dynamical systems perturbed by impulses are considered. The impulses form a flow. Over this flow the perturbed system also has the structure of a new nonautonomous/random dynamical system. The long time behavior of this system is considered. In particular the existence of an attractor is proven. The result can be applied to a large class of dissipative systems given by partial or ordinary differential equations. As an example of this class of problems the Lorenz system is studied. For another problem given by a one-dimensional affine differential equation and perturbed by affine impulses, the attractor can be calculated explicitly.
Citation: Björn Schmalfuss. Attractors for nonautonomous and random dynamical systems perturbed by impulses. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 727-744. doi: 10.3934/dcds.2003.9.727
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