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Collective-phase description of coupled oscillators with general network structure
Hiroshi Kori1, Yoji Kawamura, Hiroya Nakao
1Division of Advanced Sciences, Ochadai Academic Production, Ochanomizu University, Tokyo 112-8610, Japan. kori.hiroshi@ocha.ac.jp
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
Summary
We present a collective-phase description for coupled oscillators. This framework quantifies network sensitivity to perturbations and models interactions between multiple oscillator networks.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Network science
Background:
- Limit-cycle oscillators are fundamental in various scientific fields.
- Understanding collective behavior in coupled oscillator networks is crucial.
- Describing complex network dynamics often requires simplified models.
Purpose of the Study:
- To develop a collective-phase description for nonidentical limit-cycle oscillators with arbitrary network structures.
- To derive a general formula for collective-phase sensitivity.
- To establish an effective phase coupling description for weakly interacting multiple networks.
Main Methods:
- Developing a collective-phase variable to represent the entire network dynamics.
- Deriving a general formula for collective-phase sensitivity.
- Formulating an effective phase coupling for multiple interacting networks.
Main Results:
- A unified collective-phase description for fully phase-locked oscillator populations.
- A general formula quantifying the network's phase response to perturbations.
- An effective phase coupling model for multi-network systems.
Conclusions:
- The collective-phase description simplifies the analysis of complex oscillator networks.
- Collective-phase sensitivity provides insights into network stability and response.
- The developed framework is applicable to diverse systems of coupled oscillators.
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