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Chaotic transition in a three-coupled phase-locked loop system.

Hidekatsu Tsuruda1, Hiroyuki Shirahama, Kazuhiro Fukushima

  • 1Faculty of Education, Kumamoto University, Kumamoto 860-8555, Japan.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
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Chaotic transitions occur in coupled phase-locked loop (PLL) systems. This study observes a hybrid intermittency, combining on-off intermittency with synchronization pair recombination in chaotic systems.

Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Chaos theory

Background:

  • Phase-locked loop (PLL) systems exhibit complex behaviors.
  • Coupled oscillators can display synchronized and chaotic dynamics.
  • Intermittency is a common phenomenon in nonlinear systems.

Purpose of the Study:

  • To investigate chaotic transitions in a three-coupled PLL system.
  • To analyze intermittency phenomena, including on-off intermittency.
  • To explore chaotic transitions in coupled logistic map systems.

Main Methods:

  • Experimental observation of chaotic transitions.
  • Numerical simulations of the three-coupled PLL system.
  • Statistical analysis of on-off intermittent time series.

Related Experiment Videos

Main Results:

  • Chaotic transition observed in three-coupled PLL systems.
  • Intermittency identified in partially synchronized phases due to pair recombination.
  • Hybrid intermittency combining on-off and pair recombination types was found.
  • Chaotic transition phenomena also demonstrated in a three-coupled logistic map system.

Conclusions:

  • The three-coupled PLL system exhibits complex chaotic dynamics.
  • A novel hybrid intermittency arises from the interplay of synchronization and chaotic transitions.
  • Coupled map lattices can also display similar chaotic transition behaviors.