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Chaos in symmetric phase oscillator networks
Christian Bick1, Marc Timme, Danilo Paulikat
1Network Dynamics Group, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37073 Göttingen, Germany.
Physical Review Letters
|January 17, 2012
Summary
Symmetric systems of identical phase-coupled oscillators can exhibit chaotic dynamics and fluctuating order parameters. Nonlinear phase interactions, not inhomogeneities, can cause these chaotic instabilities in oscillatory networks.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Network Science
Background:
- Phase-coupled oscillators are fundamental models for studying synchronization in physical and biological systems.
- Previously, chaotic order parameters were observed only in systems with inhomogeneities.
Purpose of the Study:
- To investigate whether chaotic dynamics and order parameter fluctuations can arise in symmetric systems of identical oscillators.
- To determine the fundamental mechanisms driving chaos in oscillatory networks.
Main Methods:
- Theoretical analysis of phase-coupled oscillator networks.
- Mathematical modeling of nonlinear phase interactions.
- Simulation of symmetric systems with identical units.
Main Results:
- Identical, symmetric phase-coupled oscillators can exhibit chaotic dynamics.
- Chaotically fluctuating order parameters were observed even without system inhomogeneities.
- Nonlinear interactions among oscillator phases were identified as the source of instabilities.
Conclusions:
- Chaos in oscillatory networks does not require system inhomogeneities or amplitude variations.
- Nonlinear phase dynamics are sufficient to induce chaotic behavior and fluctuating order parameters.
- These findings broaden the understanding of chaos in synchronized systems.
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