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Time delay in the Kuramoto model with bimodal frequency distribution
Ernest Montbrió1, Diego Pazó, Jürgen Schmidt
1Computational Neuroscience, Technology Department, Universitat Pompeu Fabra, 08003 Barcelona, Spain.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
Summary
We studied how time delays affect coupled oscillators with bimodal frequencies. Bimodality introduces a new time scale, leading to quasiperiodic incoherence patterns in the system.
Area of Science:
- Physics
- Nonlinear Dynamics
- Complex Systems
Background:
- Coupled oscillator systems are fundamental in understanding emergent phenomena.
- Time delays in coupling can significantly alter system dynamics.
- Bimodal frequency distributions present unique challenges in synchronization studies.
Purpose of the Study:
- To investigate the impact of time-delayed all-to-all coupling on oscillator populations.
- To analyze the influence of a bimodal natural frequency distribution on synchronization.
- To characterize the parameter space for synchronized and incoherent states.
Main Methods:
- Numerical simulations of coupled oscillator networks.
- Analytical derivations for specific frequency distributions.
- Exploration of parameter space to identify solution regions.
Main Results:
- Identified distinct regions of synchronized and incoherent behavior.
- Demonstrated that bimodality introduces a novel time scale.
- Observed a quasiperiodic arrangement of incoherence regions due to this new time scale.
Conclusions:
- Time-delayed coupling in bimodal oscillator populations leads to complex dynamics.
- The introduced time scale fundamentally changes the system's coherence properties.
- Analytical and numerical methods confirm the emergence of quasiperiodic incoherence.
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