Chaos from orbit-flip homoclinic orbits generated in real systems

Hisa Aki Tanaka, Shinichi Oishi, Kazuo Horiuchi

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    A new class of chaotic systems is discovered that are generated in a practical, nonlinear, mutually coupled phase-locked loop (PLL) circuit. Presented theoretical results make it possible to understand experimental results of mutually coupled PLL's on the onset of chaos using the geometry of the invariant manifolds, while the resultant simple geometry and complex dynamics is expected to have applications in other areas, e.g., power systems or interacting bar magnets. Motivated by the numerical study of this system, the topological horseshoe is proven to be generated in the codimension 3 unfolding of a degenerated orbit-flip homoclinic point for this system. Qualitatively different type of bifurcation phenomena are also observed to appear depending on the phase detector (PD) characteristics.

    Original languageEnglish
    Title of host publicationProceedings - IEEE International Symposium on Circuits and Systems
    Editors Anon
    PublisherIEEE
    Pages263-266
    Number of pages4
    Volume1
    Publication statusPublished - 1995
    EventProceedings of the 1995 IEEE International Symposium on Circuits and Systems-ISCAS 95. Part 3 (of 3) - Seattle, WA, USA
    Duration: 1995 Apr 301995 May 3

    Other

    OtherProceedings of the 1995 IEEE International Symposium on Circuits and Systems-ISCAS 95. Part 3 (of 3)
    CitySeattle, WA, USA
    Period95/4/3095/5/3

    Fingerprint

    Phase locked loops
    Chaos theory
    Orbits
    Geometry
    Chaotic systems
    Magnets
    Detectors
    Networks (circuits)

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering
    • Electronic, Optical and Magnetic Materials

    Cite this

    Tanaka, H. A., Oishi, S., & Horiuchi, K. (1995). Chaos from orbit-flip homoclinic orbits generated in real systems. In Anon (Ed.), Proceedings - IEEE International Symposium on Circuits and Systems (Vol. 1, pp. 263-266). IEEE.

    Chaos from orbit-flip homoclinic orbits generated in real systems. / Tanaka, Hisa Aki; Oishi, Shinichi; Horiuchi, Kazuo.

    Proceedings - IEEE International Symposium on Circuits and Systems. ed. / Anon. Vol. 1 IEEE, 1995. p. 263-266.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Tanaka, HA, Oishi, S & Horiuchi, K 1995, Chaos from orbit-flip homoclinic orbits generated in real systems. in Anon (ed.), Proceedings - IEEE International Symposium on Circuits and Systems. vol. 1, IEEE, pp. 263-266, Proceedings of the 1995 IEEE International Symposium on Circuits and Systems-ISCAS 95. Part 3 (of 3), Seattle, WA, USA, 95/4/30.
    Tanaka HA, Oishi S, Horiuchi K. Chaos from orbit-flip homoclinic orbits generated in real systems. In Anon, editor, Proceedings - IEEE International Symposium on Circuits and Systems. Vol. 1. IEEE. 1995. p. 263-266
    Tanaka, Hisa Aki ; Oishi, Shinichi ; Horiuchi, Kazuo. / Chaos from orbit-flip homoclinic orbits generated in real systems. Proceedings - IEEE International Symposium on Circuits and Systems. editor / Anon. Vol. 1 IEEE, 1995. pp. 263-266
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