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Appropriate initial conditions for asymptotic descriptions of the long term evolution of dynamical systems

Published online by Cambridge University Press:  17 February 2009

A. J. Roberts
A. J. Roberts
Affiliation:
Applied Mathematics Department, University of Adelaide, S.A. 5000, Australia.
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Abstract

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A centre manifold or invariant manifold description of the evolution of a dynamical system provides a simplified view of the long term evolution of the system. In this work, I describe a procedure to estimate the appropriate starting position on the manifold which best matches an initial condition off the manifold. I apply the procedure to three examples: a simple dynamical system, a five-equation model of quasi-geostrophic flow, and shear dispersion in a channel. The analysis is also relevant to determining how best to account, within the invariant manifold description, for a small forcing in the full system.

Type
Research Article
Information
The ANZIAM Journal , Volume 31 , Issue 1 , July 1989 , pp. 48 - 75
Copyright
Copyright © Australian Mathematical Society 1989

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