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Dynamics of large oscillator populations with random interactions
Arkady Pikovsky1, Lev A Smirnov2
1Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany.
Chaos (Woodbury, N.Y.)
|July 9, 2024
Summary
We analyzed phase oscillator interactions with random couplings. Random phase shifts significantly alter coupling functions, while random strengths only renormalize interactions in large populations.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Statistical physics
Background:
- Phase oscillators are fundamental in modeling coupled systems.
- Randomness in interactions poses challenges for analytical solutions.
- Understanding coupling functions is key to predicting system behavior.
Purpose of the Study:
- To derive reduced averaged equations for large populations of phase oscillators with random coupling.
- To investigate the distinct effects of random coupling strengths and phase shifts.
- To analyze Kuramoto-Daido and Winfree coupling models.
Main Methods:
- Derivation of reduced averaged equations under statistical independence assumptions.
- Analysis of coupling functions with identical shapes but random strengths and phase shifts.
- Mathematical modeling of oscillator interactions.
Main Results:
- Effective non-random coupling terms were derived from random interactions.
- Random coupling strengths were found to renormalize interactions.
- Distributions of phase shifts in coupling were shown to reshape the coupling function.
Conclusions:
- Reduced models simplify the analysis of complex oscillator networks.
- Phase shift distributions are critical in determining the emergent behavior of coupled oscillators.
- The findings offer insights into synchronization phenomena in diverse systems.
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