Homoclinic connections and numerical integration

    Authors

    A. Tovbis

    Comments

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    Abbreviated Journal Title

    Numer. Algorithms

    Keywords

    homoclinic connection; numerical chaos; finite difference methods; DIFFERENCE SCHEME; CHAOS; Mathematics, Applied

    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.

    Journal Title

    Numerical Algorithms

    Volume

    14

    Issue/Number

    1-3

    Publication Date

    1-1-1997

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    261

    Last Page

    267

    WOS Identifier

    WOS:A1997XE68300015

    ISSN

    1017-1398

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