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Determination of the area of exponential attraction in one-dimensional finite-time systems using meshless collocation

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posted on 2023-06-09, 08:50 authored by Peter GieslPeter Giesl, James McMichen
We consider a non-autonomous ordinary differential equation over a finite time interval [T1; T2]. The area of exponential attraction consists of solutions such that the distance to adjacent solutions exponentially contracts from T1 to T2. One can use a contraction metric to determine an area of exponential attraction and to provide a bound on the rate of attraction. In this paper, we will give the first method to algorithmically construct a contraction metric for finite-time systems in one spatial dimension. We will show the existence of a contraction metric, given by a function which satisfies a second-order partial differential equation with boundary conditions. We then use meshless collocation to approximately solve this equation, and show that the resulting approximation itself defines a contraction metric, if the collocation points are sufficiently dense. We give error estimates and apply the method to an example.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Discrete and Continuous Dynamical Systems - Series B

ISSN

1531-3492

Publisher

American Institute of Mathematical Sciences

Issue

4

Volume

23

Page range

1835-1850

Department affiliated with

  • Physics and Astronomy Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-11-15

First Open Access (FOA) Date

2019-03-01

First Compliant Deposit (FCD) Date

2017-11-15

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