Cross-frequency synchronization of oscillators with time-delayed coupling.
We carry out theoretical and experimental studies of cross-frequency synchronization of two pulse oscillators with time-delayed coupling. In the theoretical part of the paper we utilize the concept of phase resetting curves and analyze the system dynamics in the case of weak coupling. We construct a Poincaré map and obtain the synchronization zones in the parameter space for m:n synchronization. To challenge the theoretical results we designed an electronic circuit implementing the coupled oscillators and studied its dynamics experimentally. We show that the developed theory predicts dynamical properties of the realistic system, including location of the synchronization zones and bifurcations inside them.
Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Street, 603950, Nizhny Novgorod, Russia and University of Nizhny Novgorod, 23 Prospekt Gagarina, 603950, Nizhny Novgorod, Russia.
Vladimir V
VV
Klinshov
Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Street, 603950, Nizhny Novgorod, Russia and University of Nizhny Novgorod, 23 Prospekt Gagarina, 603950, Nizhny Novgorod, Russia.
Dmitry S
DS
Shchapin
Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Street, 603950, Nizhny Novgorod, Russia and University of Nizhny Novgorod, 23 Prospekt Gagarina, 603950, Nizhny Novgorod, Russia.
Vladimir I
VI
Nekorkin
D004581:Electronics; D008962:Models, Theoretical; D010507:Periodicity