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