Mean field repulsive Kuramoto models: Phase locking and spatial signs
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| Vydáno v: | arXiv.org (Mar 7, 2018), p. n/a |
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| Hlavní autor: | |
| Další autoři: | , , |
| Vydáno: |
Cornell University Library, arXiv.org
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| On-line přístup: | Citation/Abstract Full text outside of ProQuest |
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| Abstrakt: | 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. |
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| ISSN: | 2331-8422 |
| Zdroj: | Engineering Database |