The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Research Article

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

A. J. Robertsa1

a1 Applied Mathematics Department, University of Adelaide, S.A. 5000, Australia.

Abstract

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.

(Received April 21 1988)

(Revised November 28 1988)