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Patterns and Stability of Coupled Multi-Stable Nonlinear Oscillators.

G Bel1,2, B S Alexandrov3, A R Bishop3

  • 1Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research and Department of Physics, Ben-Gurion University of the Negev, Sede Boqer Campus, 8499000, , Israel.

Chaos, Solitons, and Fractals
|January 16, 2023
PubMed
Summary
This summary is machine-generated.

Coupled Helmholtz-Duffing oscillators exhibit distinct stability in bi-stability regimes. Spatial perturbations lead to varied synchronization states, not solely determined by perturbation wavelength.

Keywords:
Coupled oscillatorsHelmholtz-DuffingInstabilityMulti-stabilityPatterns

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Oscillator theory

Background:

  • Nonlinear oscillators are fundamental models in physics.
  • Oscillator synchronization is a key phenomenon in coupled systems.
  • Helmholtz-Duffing oscillators exhibit bi-stability, presenting complex dynamics.

Purpose of the Study:

  • To investigate the synchronization and stability of coupled driven-damped Helmholtz-Duffing oscillators.
  • To analyze the behavior of these oscillators within bi-stability regimes.
  • To understand the influence of spatial perturbations on oscillator states.

Main Methods:

  • Numerical simulations of coupled driven-damped Helmholtz-Duffing oscillators.
  • Analysis of system response to spatially non-uniform perturbations.
  • Examination of oscillator phase configurations and stability.

Main Results:

  • Identical system parameters and driving force yield different stability for the two states against spatial perturbations.
  • The final stable states depend on factors beyond the perturbation mode's wavelength.
  • Coupled oscillators adopt diverse spatial configurations in their synchronized or desynchronized states.

Conclusions:

  • The stability of states in coupled Helmholtz-Duffing oscillators is sensitive to spatial perturbations.
  • Bi-stability regimes introduce complex synchronization behaviors.
  • Understanding these dynamics is crucial for designing and controlling coupled nonlinear systems.