TY  - JOUR
A1  - Zaks, Michael A.
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Osipov, Grigory V.
A1  - Kurths, Jürgen
T1  - Phase synchronization of chaotic oscillations in terms of periodic orbits
Y1  - 1997
SN  - 1054-1500
ER  - 
TY  - JOUR
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
A1  - Osipov, Grigory V.
A1  - Kurths, Jürgen
T1  - Phase synchronization effects in a lattice of nonidentical Rössler oscillators
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Phase synchronization of chaotic oscillators by external driving
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Osipov, Grigory V.
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Zaks, Michael A.
A1  - Kurths, Jürgen
T1  - Attractor-repeller collision and eyelet intermittency at the transition to phase synchronization
N2  - The chaotically driven circle map is considered as the simplest model ofphase synchronization of a chaotic continuous-time oscillator by external periodic force. The phase dynamics is analyzed via phase-locking regions of the periodic cycles embedded in the strange attractor. It is shown that full synchronization, where all the periodic cycles are phase locked, disappears via the attractor-repeller collision. Beyond the transition an intermittent regime with exponentially rare phase slips, resulting from the trajectory's hits on an eyelet, is observed.
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
T1  - Phase Synchronization of Chaotic Rotators
N2  - We demonstrate the existence of phase synchronization of two chaotic rotators. Contrary to phase synchronization of chaotic oscillators, here the Lyapunov exponents corresponding to both phases remain positive even in the synchronous regime. Such frequency locked dynamics with different ratios of frequencies are studied for driven continuous-time rotators and for discrete circle maps. We show that this transition to phase synchronization occurs via a crisis transition to a band-structured attractor.
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
A1  - Kurths, Jürgen
A1  - Osipov, Grigory V.
A1  - Kiss, Istvan Z.
A1  - Hudson, J. L.
T1  - Locking-based frequency measurement and synchronization of chaotic oscillators with complex dynamics
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Boccaletti, Stefano
A1  - Kurths, Jürgen
A1  - Osipov, Grigory V.
T1  - The synchronization of chaotic systems
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Osipov, Grigory V.
A1  - Kurths, Jürgen
T1  - Regular and chaotic phase synchronization of coupled circle maps
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Ivanchenko, Mikhail V.
A1  - Osipov, Grigory V.
A1  - Shalfeev, V. D.
A1  - Kurths, Jürgen
T1  - Phase synchronization in ensembles of bursting oscillators
N2  - We study the effects of mutual and external chaotic phase synchronization in ensembles of bursting oscillators. These oscillators (used for modeling neuronal dynamics) are essentially multiple time scale systems. We show that a transition to mutual phase synchronization takes place on the bursting time scale of globally coupled oscillators, while on the spiking time scale, they behave asynchronously. We also demonstrate the effect of the onset of external chaotic phase synchronization of the bursting behavior in the studied ensemble by a periodic driving applied to one arbitrarily taken neuron. We also propose an explanation of the mechanism behind this effect. We infer that the demonstrated phenomenon can be used efficiently for controlling bursting activity in neural ensembles
Y1  - 2004
SN  - 0031-9007
ER  - 
TY  - JOUR
A1  - Ivanchenko, Mikhail V.
A1  - Osipov, Grigory V.
A1  - Shalfeev, V. D.
A1  - Kurths, Jürgen
T1  - Phase synchronization of chaotic intermittent oscillations
N2  - We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization
Y1  - 2004
SN  - 0031-9007
ER  -