Title

Homoclinic connections and numerical integration

Keywords

Finite difference methods; Homoclinic connection; Numerical chaos

Abstract

One of the best known mechanisms of onset of chaotic motion is breaking of heteroclinic and homoclinic connections. It is well known that numerical integration on long time intervals very often becomes unstable (numerical instabilities) and gives rise to what is called "numerical chaos". As one of the initial steps to discuss this phenomenon, we show in this paper that Euler's finite difference scheme does not preserve homoclinic connections.

Publication Date

1-1-1997

Publication Title

Numerical Algorithms

Volume

14

Issue

1-3

Number of Pages

261-267

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1023/a:1019121231815

Socpus ID

0031517068 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0031517068

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