Heteroclinic Synchronization: Ultrasubharmonic Locking

Mikhail I. Rabinovich, Ramón Huerta, Pablo Varona
2006 Physical Review Letters  
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
more » ... teroclinic 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.
doi:10.1103/physrevlett.96.014101 pmid:16486458 fatcat:vuojqfsdnnhbbdbicwd6qpgtsy