Heteroclinic synchronization: ultrasubharmonic locking.
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.
Rabinovich
Mikhail I
MI
Institute for Nonlinear Science, University of California-San Diego, 9500 Gilman Drive 0402, La Jolla, California 92093, USA. mrabinovich@ucsd.edu
Huerta
Ramón
R
Varona
Pablo
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D000818:Animals; D001921:Brain / Q000502:physiology*; D003344:Cortical Synchronization; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*