Hierarchy of exact low-dimensional reductions for populations of coupled oscillators
arXiv:2108.10143 · doi:10.1103/PhysRevLett.128.054101
Abstract
We consider an ensemble of phase oscillators in the thermodynamic limit, where it is described by a kinetic equation for the phase distribution density. We propose an ansatz for the circular moments of the distribution (Kuramoto-Daido order parameters) that allows for an exact truncation at an arbitrary number of modes. In the simplest case of one mode, the ansatz coincides with that of Ott and Antonsen [Chaos 18, 037113 (2008)]. Dynamics on the extended manifolds facilitate higher dimensional behavior such as chaos, which we demonstrate with a simulation of a Josephson junction array. The findings are generalized for oscillators with a Cauchy-Lorentzian distribution of natural frequencies.
arXiv comment5 pages, 2 figures; published version, cosmetic changes only
References in corpus (24)
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
- Solvable model for chimera states of coupled oscillators
- Long Time Evolution of Phase Oscillator Systems
- Macroscopic description for networks of spiking neurons
- Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
- Partially integrable dynamics of hierarchical populations of coupled oscillators
- Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
- Phase oscillators with global sinusoidal coupling evolve by Mobius group action
- Self-Emerging and Turbulent Chimeras in Oscillator Chains
- Dynamics of noisy oscillator populations beyond the Ott-Antonsen ansatz
- Invariant submanifold for series arrays of Josephson junctions
- Glassy states and superrelaxation in populations of coupled phase oscillators
- A reduction methodology for fluctuation driven population dynamics
- Ott-Antonsen attractiveness for parameter-dependent oscillatory networks
- Synchronization of a Josephson junction array in terms of global variables
- Is the Ott-Antonsen manifold attracting?
- Collective synchronization in the presence of reactive coupling and shear diversity
- Synchronization of oscillators in a Kuramoto-type model with generic coupling
- Ott-Antonsen ansatz is the only admissible truncation of a circular cumulant series
- Chimera states in small disordered optomechanical arrays
- Low-dimensional description for ensembles of identical phase oscillators subject to Cauchy noise
- The Kuramoto model with distributed shear
- Low-dimensional dynamics of phase oscillators driven by Cauchy noise
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