On synchronization in Kuramoto models on spheres
arXiv:2110.14719 · doi:10.1007/s13324-021-00567-4
Abstract
We analyze two classes of Kuramoto models on spheres that have been introduced in previous studies. Our analysis is restricted to ensembles of identical oscillators with the global coupling. In such a setup, with an additional assumption that the initial distribution of oscillators is uniform on the sphere, one can derive equations for order parameters in closed form. The rate of synchronization in a real Kuramoto model depends on the dimension of the sphere. Specifically, synchronization is faster on higher-dimensional spheres. On the other side, real order parameter in complex Kuramoto models always satisfies the same ODE, regardless of the dimension. The derivation of equations for real order parameters in Kuramoto models on spheres is based on recently unveiled connections of these models with geometries of unit balls. Simulations of the system with several hundreds of oscillators yield perfect fits with the theoretical predictions, that are obtained by solving equations for the order parameter.
References in corpus (8)
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Phase oscillators with global sinusoidal coupling evolve by Mobius group action
- Continuous versus Discontinuous Transitions in the -Dimensional Generalized Kuramoto Model: Odd is Different
- Solvable model of the collective motion of heterogeneous particles interacting on a sphere
- Hyperbolic Geometry of Kuramoto Oscillator Networks
- Complexity Reduction Ansatz for Systems of Interacting Orientable Agents: Beyond The Kuramoto Model
- Dynamics of the Kuramoto-Sakaguchi Oscillator Network with Asymmetric Order Parameter
- Phase Synchronization of non-Abelian Oscillators on Small-World Networks