Chaos from orbit-flip homoclinic orbits generated in real systems

Hisa Aki Tanaka*, Shin'ichi Oishi, Kazuo Horiuchi

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


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
Pages (from-to)263-266
Number of pages4
JournalProceedings - IEEE International Symposium on Circuits and Systems
Publication statusPublished - 1995 Jan 1
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

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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