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Fast phase randomization via two-folds.

D J W Simpson1, M R Jeffrey2

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PubMed
Summary
This summary is machine-generated.

Invisible two-folds, or Teixeira singularities, in vector fields can randomize oscillator phase. This study reveals how nonlinear dynamics influence phase probability and demonstrates a fast method for desynchronizing oscillators using these singularities.

Keywords:
Filippov systemdesynchronizationpiecewise-smoothsliding motion

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Area of Science:

  • Dynamical systems theory
  • Nonlinear dynamics
  • Chaos theory

Background:

  • A two-fold is a singular point on a discontinuity surface of a piecewise-smooth vector field.
  • Invisible two-folds (Teixeira singularities) can lead to unpredictable asymptotic phases in dynamical systems.

Purpose of the Study:

  • To investigate the dependence of asymptotic phase probability distribution on global nonlinear dynamics.
  • To demonstrate a method for randomizing the phase of a smooth oscillator using invisible two-folds.
  • To propose the use of invisible two-folds for fast desynchronization of oscillator collections.

Main Methods:

  • Analysis of global nonlinear dynamics in relation to phase probability distributions.
  • Design of a discontinuous control law to generate invisible two-folds.
  • Comparison of phase randomization speed with existing methods.

Main Results:

  • The probability distribution of the asymptotic phase is shown to depend on global nonlinear dynamics.
  • A simple discontinuous control law successfully generates an invisible two-fold, randomizing oscillator phase.
  • Phase randomization via invisible two-folds is demonstrated to be faster than methods using fixed points.

Conclusions:

  • Invisible two-folds offer a novel mechanism for controlling and randomizing the phase of oscillators.
  • The proposed control law provides an efficient method for desynchronizing collections of oscillators.
  • This approach leverages unique properties of two-folds for rapid dynamical control.