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Heteroclinic synchronization: ultrasubharmonic locking.

Mikhail I Rabinovich·Ramón Huerta·Pablo Varona
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Abstract

According to the traditional view of synchronization, a weak periodic input is able to lock a nonlinear oscillator at a frequency close to that of the input (1:1 zone). If the forcing increases, it is possible to achieve synchronization at subharmonic bands also. Using a competitive dynamical system we show the inverse phenomenon: with a weak signal the 1:1 zone is narrow, but the synchronization of ultrasubharmonics is dominant. In the system's phase space, there exists a heteroclinic contour in the autonomous regime, which is the image of sequential dynamics. Under the action of a weak periodic forcing, in the vicinity of the contour a stable limit cycle with long period appears. This results in the locking of very low-frequency oscillations with the finite frequency of the forcing. We hypothesize that this phenomenon can be the origin for the synchronization of slow and fast brain rhythms.

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AnimalsBrainCortical SynchronizationModels, NeurologicalNeuronsJournal ArticleResearch Support, N.I.H., ExtramuralResearch Support, Non-U.S. Gov'tResearch Support, U.S. Gov't, Non-P.H.S.

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BibTeXRIS

Mikhail I Rabinovich, Ramón Huerta, Pablo Varona. 2006-01-04. Heteroclinic synchronization: ultrasubharmonic locking.. https://doi.org/10.1103/physrevlett.96.014101

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