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Synchronization of coupled active rotators by common noise.
Anastasiya V Dolmatova1, Denis S Goldobin1,2, Arkady Pikovsky3,4
1Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, 614013 Perm, Russia.
Physical Review. E
|January 20, 2018
Summary
Common noise synchronizes coupled active rotators, but repulsive coupling can lead to partial synchrony or frequency repulsion, revealing a power law in this phenomenon.
Area of Science:
- Physics
- Nonlinear Dynamics
- Statistical Mechanics
Background:
- Coupled active rotators are fundamental models in physics and biology.
- Noise typically enhances synchrony in such systems.
- Coupling can be attractive (promoting synchrony) or repulsive (hindering synchrony).
Purpose of the Study:
- To investigate the impact of common noise on coupled active rotators with both attractive and repulsive coupling.
- To analyze the transition from full to partial synchrony in identical rotators.
- To explore complex synchronization phenomena in non-identical rotators.
Main Methods:
- Development of an analytical approach using angle-action variables.
- Averaging over fast rotational dynamics.
- Mathematical analysis of system behavior under varying coupling strengths and noise levels.
Main Results:
- Common noise facilitates synchrony, regardless of coupling type.
- Identical rotators exhibit a transition from full to partial synchrony at a critical repulsive coupling value.
- Non-identical rotators display phase locking alongside frequency repulsion (anti-entrainment) at moderate repulsive coupling.
- Frequency repulsion follows a nontrivial power law.
Conclusions:
- Repulsive coupling introduces complex dynamics, including partial synchrony and anti-entrainment, in the presence of common noise.
- The observed power law for frequency repulsion offers new insights into nonlinear system behavior.
- This study elucidates the intricate interplay between noise, coupling, and synchrony in active rotator systems.
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