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Time and frequency -Domain Interpretation of Phase-lead Control01:24

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Controlling phase multistability in coupled period-doubling oscillators.

A V Shabunin1

  • 1Radiophysics and Nonlinear Dynamics Department, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russian Federation.

Chaos (Woodbury, N.Y.)
|April 6, 2013
PubMed
Summary

Researchers developed a simple method to switch between states in coupled oscillators. This technique uses two periodic forces to control oscillation phases, effectively managing system behavior for periodic and chaotic attractors.

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Area of Science:

  • Nonlinear Dynamics
  • Control Theory
  • Complex Systems

Background:

  • Coupled oscillators exhibit complex behaviors, including multiple coexisting attractors.
  • Switching between these attractors is crucial for controlling system dynamics.
  • Existing methods for attractor switching can be complex or limited in scope.

Purpose of the Study:

  • To propose a simple and effective method for switching between coexisting attractors in coupled nonlinear oscillators.
  • To demonstrate the control mechanism using periodic forces.
  • To validate the method's efficiency for both periodic and chaotic attractors.

Main Methods:

  • A control strategy based on applying two external periodic forces to coupled oscillators.
  • The forces are designed to "pull" the phases of the oscillations to desired values.
  • Key control parameters include the frequency and phase-shift of the applied forces.

Main Results:

  • The proposed method successfully switches between coexisting attractors in a system of two coupled period-doubling oscillators.
  • The frequency and phase-shift of the external forces were identified as critical parameters determining the resulting dynamical regime.
  • The method proved effective for coupled Chua's oscillators, demonstrating control over both periodic and chaotic attractors.

Conclusions:

  • A straightforward and efficient method for controlling attractor switching in coupled nonlinear systems has been presented.
  • The technique offers a novel approach to manipulating complex dynamics in oscillatory systems.
  • The findings have potential applications in various fields involving coupled oscillators, such as electronics and biology.