Mean field repulsive Kuramoto models: Phase locking and spatial signs
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| Publicat a: | arXiv.org (Mar 7, 2018), p. n/a |
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| Altres autors: | , , |
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Cornell University Library, arXiv.org
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| Accés en línia: | Citation/Abstract Full text outside of ProQuest |
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| 001 | 2071720338 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2331-8422 | ||
| 035 | |a 2071720338 | ||
| 045 | 0 | |b d20180307 | |
| 100 | 1 | |a Ciobotaru, Corina | |
| 245 | 1 | |a Mean field repulsive Kuramoto models: Phase locking and spatial signs | |
| 260 | |b Cornell University Library, arXiv.org |c Mar 7, 2018 | ||
| 513 | |a Working Paper | ||
| 520 | 3 | |a 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. | |
| 653 | |a Ordinary differential equations | ||
| 653 | |a Transformations (mathematics) | ||
| 653 | |a Covariance matrix | ||
| 653 | |a Nonparametric statistics | ||
| 653 | |a Data processing | ||
| 653 | |a Mathematical analysis | ||
| 653 | |a Constraining | ||
| 653 | |a Differential geometry | ||
| 653 | |a Initial conditions | ||
| 653 | |a Locking | ||
| 653 | |a Matrix methods | ||
| 653 | |a Synchronism | ||
| 653 | |a Matrix algebra | ||
| 653 | |a Differential equations | ||
| 653 | |a Robustness (mathematics) | ||
| 653 | |a Statistical inference | ||
| 653 | |a Phase transitions | ||
| 700 | 1 | |a Linard Hoessly | |
| 700 | 1 | |a Mazza, Christian | |
| 700 | 1 | |a Xavier, Richard | |
| 773 | 0 | |t arXiv.org |g (Mar 7, 2018), p. n/a | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/2071720338/abstract/embedded/L8HZQI7Z43R0LA5T?source=fedsrch |
| 856 | 4 | 0 | |3 Full text outside of ProQuest |u http://arxiv.org/abs/1803.02647 |