The Ontario Research Centre for Computer Algebra

# The UWO ORCCA Reading Room

## UWO ORCCA TR-00-15 Summary

Computation of Center Manifolds, Nov 11, 2000, Robert Corless, Keith Geddes and Xianping Liu, 12 pages.

Abstract:

We present a method to compute center manifolds for dynamical systems ${\bf \dot{x}} = {\bf f}({\bf x}, \mu), ({\bf x} \in {\bf R}^n, \mu \in {\bf R}^p)$, where $x$ is a vector of state variables and $\mu$ is a vector of parameters. Explicit formulae are derived and implemented in Maple. This enables one to compute center manifolds to any order easily. We also show how to analyze the errors of the analytical approximations, and how they depend on the parameters, by computing the \textsl{residual} or \textsl{defect}. Several examples are given to show the applicability of the program.
This method should be of interest to the Computer Algebra community as a test-bed for several different sets of Computer Algebra tools, namely transformations, linear algebra, and series.