A flexible error estimate for the application of centre manifold theory

TL;DR

This paper extends centre manifold theory to provide more adaptable error estimates, enabling better evaluation of low-dimensional models at finite parameters by allowing different approximation orders in parameters and variables.

Contribution

It introduces a generalized error estimation framework that accommodates differing approximation orders in parameters and dynamical variables.

Findings

Extended the theory to handle different approximation orders

Improved evaluation of low-dimensional models at finite parameters

Provided a more flexible error estimation method

Abstract

In applications of centre manifold theory we need more flexible error estimates than that provided by, for example, the Approximation Theorem~3 by Carr (1981,1983). Here we extend the theory to cover the case where the order of approximation in parameters and that in dynamical variables may be completely different. This allows, for example, the effective evaluation of low-dimensional dynamical models at finite parameter values.