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Dynamics of oscillators globally coupled via two mean fields
Xiyun Zhang1,2, Arkady Pikovsky3,4, Zonghua Liu5
1Department of Physics, East China Normal University, Shanghai, 200062, P. R. China. zxy_822@126.com.
Scientific Reports
|May 20, 2017
Summary
This study explores coupled oscillator synchronization using two competing mean fields. Complex dynamics and novel states emerge when coupling channels conflict, offering insights into natural oscillatory systems.
Area of Science:
- Physics
- Nonlinear Dynamics
- Complex Systems
Background:
- Classical Kuramoto model studies oscillator synchronization via a single mean field.
- Understanding complex dynamics in coupled oscillatory systems is crucial.
Purpose of the Study:
- To investigate the synchronization properties of Kuramoto-type phase oscillators coupled via two mean fields.
- To analyze the stability of incoherent states and traveling wave solutions under competing coupling.
- To characterize novel dynamical states arising from the interplay of synchronizing and desynchronizing fields.
Main Methods:
- Derivation of stability properties for the incoherent state.
- Numerical analysis of traveling wave solutions and their stability.
- Identification and characterization of normal, anomalous, and hybrid branches of solutions.
Main Results:
- Two competing mean fields can lead to complex system behavior, including traveling waves with distinct locking patterns.
- Nontrivial states predominantly emerge when the two fields have opposing effects (synchronization vs. desynchronization).
- Anomalous and hybrid branches, beyond typical bifurcations, are identified, alongside modulated quasiperiodic dynamics when stable traveling waves are absent.
Conclusions:
- The competition between two coupling channels significantly enriches the dynamics of coupled oscillator systems.
- This generalized framework provides new perspectives for understanding complex phenomena in various natural oscillatory systems.
- The study highlights the importance of considering multiple, potentially conflicting, coupling mechanisms.
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