Singular point analysis for dynamical systems with many parameters‐an application to an asymmetrically and densely connected neural network model

Hisa‐Aki ‐A Tanaka, Atsushi Okada, Kazuo Horiuchi, Shinichi Oishi

    Research output: Contribution to journalArticle

    Abstract

    In the nonlinear dynamical system, the singular point analysis (Painleve test) is known to be an analytic method for identifying integrable systems or characterizing chaos. In this paper, nonlinear dynamical networks, which are simplified models for mutually connected analog neurons, are studied mainly in terms of the singular point analysis by introducing the complex time. The following results were obtained: 1) some conditions for integrability and first integrals are identified; 2) as an application of Yoshida's theorem, it is proven that many cases in our system are (algebraically) noninegrable; 3) a self‐validated numerical algorithm is proposed to overcome some difficulties known to appear in applying the singular point analysis (Yoshida's theorem) to higher‐order systems.

    Original languageEnglish
    Pages (from-to)92-102
    Number of pages11
    JournalElectronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
    Volume77
    Issue number10
    DOIs
    Publication statusPublished - 1994

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    Nonlinear dynamical systems
    Chaos theory
    Neurons
    Dynamical systems
    Neural networks

    Keywords

    • high dimensional dynamical system
    • nonlinear dynamical network
    • self‐validating numerics
    • Singular point analysis

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering

    Cite this

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    title = "Singular point analysis for dynamical systems with many parameters‐an application to an asymmetrically and densely connected neural network model",
    abstract = "In the nonlinear dynamical system, the singular point analysis (Painleve test) is known to be an analytic method for identifying integrable systems or characterizing chaos. In this paper, nonlinear dynamical networks, which are simplified models for mutually connected analog neurons, are studied mainly in terms of the singular point analysis by introducing the complex time. The following results were obtained: 1) some conditions for integrability and first integrals are identified; 2) as an application of Yoshida's theorem, it is proven that many cases in our system are (algebraically) noninegrable; 3) a self‐validated numerical algorithm is proposed to overcome some difficulties known to appear in applying the singular point analysis (Yoshida's theorem) to higher‐order systems.",
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    author = "Tanaka, {Hisa‐Aki ‐A} and Atsushi Okada and Kazuo Horiuchi and Shinichi Oishi",
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    AU - Tanaka, Hisa‐Aki ‐A

    AU - Okada, Atsushi

    AU - Horiuchi, Kazuo

    AU - Oishi, Shinichi

    PY - 1994

    Y1 - 1994

    N2 - In the nonlinear dynamical system, the singular point analysis (Painleve test) is known to be an analytic method for identifying integrable systems or characterizing chaos. In this paper, nonlinear dynamical networks, which are simplified models for mutually connected analog neurons, are studied mainly in terms of the singular point analysis by introducing the complex time. The following results were obtained: 1) some conditions for integrability and first integrals are identified; 2) as an application of Yoshida's theorem, it is proven that many cases in our system are (algebraically) noninegrable; 3) a self‐validated numerical algorithm is proposed to overcome some difficulties known to appear in applying the singular point analysis (Yoshida's theorem) to higher‐order systems.

    AB - In the nonlinear dynamical system, the singular point analysis (Painleve test) is known to be an analytic method for identifying integrable systems or characterizing chaos. In this paper, nonlinear dynamical networks, which are simplified models for mutually connected analog neurons, are studied mainly in terms of the singular point analysis by introducing the complex time. The following results were obtained: 1) some conditions for integrability and first integrals are identified; 2) as an application of Yoshida's theorem, it is proven that many cases in our system are (algebraically) noninegrable; 3) a self‐validated numerical algorithm is proposed to overcome some difficulties known to appear in applying the singular point analysis (Yoshida's theorem) to higher‐order systems.

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