TY  - JOUR
A1  - Politi, Antonio
A1  - Rosenblum, Michael
T1  - Equivalence of phase-oscillator and integrate-and-fire models
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - A quantitative comparison of various classes of oscillators (integrate-and-fire, Winfree, and Kuramoto-Daido type) is performed in the weak-coupling limit for a fully connected network of identical units. An almost perfect agreement is found, with only tiny differences among the models. We also show that the regime of self-consistent partial synchronization is rather general and can be observed for arbitrarily small coupling strength in any model class. As a byproduct of our study, we are able to show that an integrate-and-fire model with a generic pulse shape can be always transformed into a similar model with delta pulses and a suitable phase response curve.
Y1  - 2015
U6  - https://doi.org/10.1103/PhysRevE.91.042916
SN  - 1539-3755
SN  - 1550-2376
VL  - 91
IS  - 4
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Perez-Velazquez, Jose Luis
A1  - Erra, Ramon Guevara
A1  - Rosenblum, Michael
T1  - The Epileptic Thalamocortical Network is a Macroscopic Self-Sustained Oscillator: Evidence from Frequency-Locking Experiments in Rat Brains
JF  - Scientific reports
N2  - The rhythmic activity observed in nervous systems, in particular in epilepsies and Parkinson's disease, has often been hypothesized to originate from a macroscopic self-sustained neural oscillator. However, this assumption has not been tested experimentally. Here we support this viewpoint with in vivo experiments in a rodent model of absence seizures, by demonstrating frequency locking to external periodic stimuli and finding the characteristic Arnold tongue. This result has important consequences for developing methods for the control of brain activity, such as seizure cancellation.
Y1  - 2015
U6  - https://doi.org/10.1038/srep08423
SN  - 2045-2322
VL  - 5
PB  - Nature Publ. Group
CY  - London
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
T1  - Two types of quasiperiodic partial synchrony in oscillator ensembles
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We analyze quasiperiodic partially synchronous states in an ensemble of Stuart-Landau oscillators with global nonlinear coupling. We reveal two types of such dynamics: in the first case the time-averaged frequencies of oscillators and of the mean field differ, while in the second case they are equal, but the motion of oscillators is additionally modulated. We describe transitions from the synchronous state to both types of quasiperiodic dynamics, and a transition between two different quasiperiodic states. We present an example of a bifurcation diagram, where we show the borderlines for all these transitions, as well as domain of bistability.
Y1  - 2015
U6  - https://doi.org/10.1103/PhysRevE.92.012919
SN  - 1539-3755
SN  - 1550-2376
VL  - 92
IS  - 1
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
T1  - Dynamics of globally coupled oscillators: Progress and perspectives
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - In this paper, we discuss recent progress in research of ensembles of mean field coupled oscillators. Without an ambition to present a comprehensive review, we outline most interesting from our viewpoint results and surprises, as well as interrelations between different approaches. (c) 2015 AIP Publishing LLC.
Y1  - 2015
U6  - https://doi.org/10.1063/1.4922971
SN  - 1054-1500
SN  - 1089-7682
VL  - 25
IS  - 9
PB  - American Institute of Physics
CY  - Melville
ER  -