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