Invariant Manifolds for Random Dynamical Systems with Slow and Fast Variables |
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Authors: | Björn Schmalfuss Klaus R Schneider |
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Institution: | (1) Institute for Mathematics, University of Paderborn, Warburger Strasse 100, 05251 Paderborn, Germany;(2) Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany |
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Abstract: | We consider random dynamical systems with slow and fast variables driven by two independent metric dynamical systems modeling
stochastic noise. We establish the existence of a random inertial manifold eliminating the fast variables. If the scaling
parameter tends to zero, the inertial manifold tends to another manifold which is called the slow manifold. We achieve our
results by means of a fixed point technique based on a random graph transform. To apply this technique we need an asymptotic
gap condition.
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Keywords: | Random dynamical systems fast– slow system slow manifold inertial manifold |
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