Numerical verification method of existence of connecting orbits for continuous dynamical systems

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    In this paper, a numerical method is presented for proving the existence and inclusion of connecting orbits of continuous dynamical systems described by parameterized nonlinear ordinary differential equations. Taking a certain second order nonlinear ordinary differential equaiton as an example, the existence of homoclinic bifurcation points is proved by the method.

    Original languageEnglish
    Pages (from-to)193-201
    Number of pages9
    JournalJournal of Universal Computer Science
    Volume4
    Issue number2
    Publication statusPublished - 1998

    Fingerprint

    Connecting Orbits
    Numerical Verification
    Ordinary differential equations
    Numerical methods
    Dynamical systems
    Orbits
    Dynamical system
    Homoclinic Point
    Homoclinic Bifurcation
    Bifurcation Point
    Nonlinear Ordinary Differential Equations
    Inclusion
    Numerical Methods

    Keywords

    • Connecting Orbits
    • Defining Equation of Stable-Manifolds
    • Numerical Verification of Existence of Nonlinear boundary Value Problems

    ASJC Scopus subject areas

    • Computer Science(all)

    Cite this

    @article{427b3a3cd9074115a9c820bb4f8dba96,
    title = "Numerical verification method of existence of connecting orbits for continuous dynamical systems",
    abstract = "In this paper, a numerical method is presented for proving the existence and inclusion of connecting orbits of continuous dynamical systems described by parameterized nonlinear ordinary differential equations. Taking a certain second order nonlinear ordinary differential equaiton as an example, the existence of homoclinic bifurcation points is proved by the method.",
    keywords = "Connecting Orbits, Defining Equation of Stable-Manifolds, Numerical Verification of Existence of Nonlinear boundary Value Problems",
    author = "Shinichi Oishi",
    year = "1998",
    language = "English",
    volume = "4",
    pages = "193--201",
    journal = "Journal of Universal Computer Science",
    issn = "0948-695X",
    publisher = "Springer Verlag",
    number = "2",

    }

    TY - JOUR

    T1 - Numerical verification method of existence of connecting orbits for continuous dynamical systems

    AU - Oishi, Shinichi

    PY - 1998

    Y1 - 1998

    N2 - In this paper, a numerical method is presented for proving the existence and inclusion of connecting orbits of continuous dynamical systems described by parameterized nonlinear ordinary differential equations. Taking a certain second order nonlinear ordinary differential equaiton as an example, the existence of homoclinic bifurcation points is proved by the method.

    AB - In this paper, a numerical method is presented for proving the existence and inclusion of connecting orbits of continuous dynamical systems described by parameterized nonlinear ordinary differential equations. Taking a certain second order nonlinear ordinary differential equaiton as an example, the existence of homoclinic bifurcation points is proved by the method.

    KW - Connecting Orbits

    KW - Defining Equation of Stable-Manifolds

    KW - Numerical Verification of Existence of Nonlinear boundary Value Problems

    UR - http://www.scopus.com/inward/record.url?scp=33947280550&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=33947280550&partnerID=8YFLogxK

    M3 - Article

    AN - SCOPUS:33947280550

    VL - 4

    SP - 193

    EP - 201

    JO - Journal of Universal Computer Science

    JF - Journal of Universal Computer Science

    SN - 0948-695X

    IS - 2

    ER -