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Phase-response curves of coupled oscillators
Tae-Wook Ko1, G Bard Ermentrout
1Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA. taewook.ko@gmail.com
Summary
Coupling significantly impacts how oscillators respond to stimuli. This study analytically derives phase-response curves (PRCs) for coupled oscillators, revealing how interactions modify their behavior.
Area of Science:
- Nonlinear dynamics
- Systems biology
- Physics
Background:
- Real-world oscillators are frequently coupled.
- Coupling influences oscillator responses to external stimuli.
- Understanding coupled oscillator dynamics is crucial in various scientific fields.
Purpose of the Study:
- To investigate the phase-response curves (PRCs) of coupled oscillators.
- To analytically determine PRCs for weakly coupled phase-locked oscillators.
- To discuss PRCs for globally coupled oscillators using simulations and analytical methods.
Main Methods:
- Analytical derivation of PRCs for two weakly coupled phase-locked oscillators.
- Utilizing the PRC of uncoupled oscillators and the system's coupling function.
- Employing simulation and analytical techniques to examine globally coupled oscillators.
Main Results:
- Formulas for PRCs of weakly coupled phase-locked oscillators were obtained.
- The influence of coupling on oscillator response was quantified.
- PRCs for globally coupled systems were explored.
Conclusions:
- Coupling functions and uncoupled oscillator PRCs determine coupled oscillator PRCs.
- Analytical and simulation methods provide insights into coupled oscillator behavior.
- This work offers a framework for analyzing complex oscillatory systems.
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