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Cooperative dynamics in a class of coupled two-dimensional oscillators
J A Acebrón1, W-J Rappel, A R Bulsara
1Department of Physics, University of California, San Diego, La Jolla, California 92093, USA. acebron@physics.ucsd.edu
Summary
This study investigates coupled nonlinear oscillators, like superconducting quantum interference devices (SQUIDs), and their transition to oscillations. We found that coupling strength and noise affect oscillation frequency, enabling more sensitive SQUID detection.
Area of Science:
- Nonlinear Dynamics
- Quantum Electronics
- Complex Systems
Background:
- Nonlinear oscillators exhibit complex behaviors, including saddle-node bifurcations where stable states disappear.
- The two-junction superconducting quantum interference device (SQUID) serves as a model system for studying these phenomena.
Purpose of the Study:
- To analyze the dynamics of globally coupled nonlinear oscillators, focusing on the transition to spontaneous oscillations.
- To investigate the influence of coupling parameters and noise on the system's oscillation frequency.
- To explore the potential for enhanced SQUID-based detection systems.
Main Methods:
- Utilized an extension of center-manifold reduction for deterministic analysis.
- Employed a mean-field description leading to a nonlinear Fokker-Planck equation for noisy systems.
- Applied a weak external sinusoidal probe signal to determine system frequency via classical resonance.
Main Results:
- Oscillation frequency is dependent on coupling strength and the number of oscillators, decreasing with increased coupling.
- The nonlinear Fokker-Planck equation was investigated for realistic noise levels.
- Classical resonance successfully determined the underlying frequency of the noisy system.
Conclusions:
- The study explains previously observed experimental results in coupled oscillator systems.
- The findings suggest a pathway for designing more sensitive SQUID-based detection systems by leveraging resonance phenomena.