Chaos in Kuramoto oscillator networks

DOI10.1063/1.5041444zbMath1396.34019arXiv1802.05481OpenAlexW2786531265WikidataQ90708582 ScholiaQ90708582MaRDI QIDQ4683657

Mark J. Panaggio, Christian Bick, Erik Andreas Martens

Publication date: 21 September 2018

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.05481

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Qualitative investigation and simulation of ordinary differential equation models (34C60) Complex behavior and chaotic systems of ordinary differential equations (34C28)

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Uses Software

• AUTO2000

Cites Work

• The Kuramoto model in complex networks
• Dynamics of heterogeneous oscillator ensembles in terms of collective variables
• Isotropy of angular frequencies and weak chimeras with broken symmetry
• Chemical oscillations, waves, and turbulence
• Time-reversal symmetry in dynamical systems: a survey
• Turbulence in the Ott–Antonsen equation for arrays of coupled phase oscillators
• Chaotic weak chimeras and their persistence in coupled populations of phase oscillators
• Dynamics of weakly inhomogeneous oscillator populations: perturbation theory on top of Watanabe–Strogatz integrability
• Weak chimeras in minimal networks of coupled phase oscillators
• The asymptotic behavior of the order parameter for the infinite-N Kuramoto model
• Integrability of a globally coupled oscillator array
• Chaos in generically coupled phase oscillator networks with nonpairwise interactions
• Chimera states in two populations with heterogeneous phase-lag
• Low dimensional behavior of large systems of globally coupled oscillators
• Long time evolution of phase oscillator systems
• Identical phase oscillators with global sinusoidal coupling evolve by Möbius group action
• Generating macroscopic chaos in a network of globally coupled phase oscillators

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