Generating macroscopic chaos in a network of globally coupled phase oscillators
arXiv:1108.0038 · doi:10.1063/1.3638441
Abstract
We consider an infinite network of globally-coupled phase oscillators in which the natural frequencies of the oscillators are drawn from a symmetric bimodal distribution. We demonstrate that macroscopic chaos can occur in this system when the coupling strength varies periodically in time. We identify period-doubling cascades to chaos, attractor crises, and horseshoe dynamics for the macroscopic mean field. Based on recent work that clarified the bifurcation structure of the static bimodal Kuramoto system, we qualitatively describe the mechanism for the generation of such complicated behavior in the time varying case.
References in corpus (9)
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
- Partially integrable dynamics of hierarchical populations of coupled oscillators
- Chimera states in heterogeneous networks
- Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
- External Periodic Driving of Large Systems of Globally Coupled Phase Oscillators
- Invariant submanifold for series arrays of Josephson junctions
- Time delay in the Kuramoto model with bimodal frequency distribution
- Lyapunov analysis captures the collective dynamics of large chaotic systems
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