Mean field repulsive Kuramoto models: Phase locking and spatial signs
Guardado en:
| Udgivet i: | arXiv.org (Mar 7, 2018), p. n/a |
|---|---|
| Hovedforfatter: | |
| Andre forfattere: | , , |
| Udgivet: |
Cornell University Library, arXiv.org
|
| Fag: | |
| Online adgang: | Citation/Abstract Full text outside of ProQuest |
| Tags: |
Ingen Tags, Vær først til at tagge denne postø!
|
| Resumen: | The phenomenon of self-synchronization in populations of oscillatory units appears naturally in neurosciences. However, in some situations, the formation of a coherent state is damaging. In this article we study a repulsive mean-field Kuramoto model that describes the time evolution of n points on the unit circle, which are transformed into incoherent phase-locked states. It has been recently shown that such systems can be reduced to a three-dimensional system of ordinary differential equations, whose mathematical structure is strongly related to hyperbolic geometry. The orbits of the Kuramoto dynamical system are then described by a ow of M\"obius transformations. We show this underlying dynamic performs statistical inference by computing dynamically M-estimates of scatter matrices. We also describe the limiting phase-locked states for random initial conditions using Tyler's transformation matrix. Moreover, we show the repulsive Kuramoto model performs dynamically not only robust covariance matrix estimation, but also data processing: the initial configuration of the n points is transformed by the dynamic into a limiting phase-locked state that surprisingly equals the spatial signs from nonparametric statistics. That makes the sign empirical covariance matrix to equal 1 2 id2, the variance-covariance matrix of a random vector that is uniformly distributed on the unit circle. |
|---|---|
| ISSN: | 2331-8422 |
| Fuente: | Engineering Database |