TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
T1  - Numerical phase reduction beyond the first order approximation
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for the evolution of the phase. Our simulations demonstrate that the description of the dynamics solely by phase variables can be valid for rather strong coupling strengths and large deviations from the limit cycle. Coupling functions depend crucially on the coupling and are generally non-decomposable in phase response and forcing terms. We also discuss the limitations of the approach. Published under license by AIP Publishing.
Y1  - 2019
U6  - https://doi.org/10.1063/1.5079617
SN  - 1054-1500
SN  - 1089-7682
VL  - 29
IS  - 1
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Teichmann, Erik
A1  - Rosenblum, Michael
T1  - Solitary states and partial synchrony in oscillatory ensembles with attractive and repulsive interactions
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - We numerically and analytically analyze transitions between different synchronous states in a network of globally coupled phase oscillators with attractive and repulsive interactions. The elements within the attractive or repulsive group are identical, but natural frequencies of the groups differ. In addition to a synchronous two-cluster state, the system exhibits a solitary state, when a single oscillator leaves the cluster of repulsive elements, as well as partially synchronous quasiperiodic dynamics. We demonstrate how the transitions between these states occur when the repulsion starts to prevail over attraction.
Y1  - 2019
U6  - https://doi.org/10.1063/1.5118843
SN  - 1054-1500
SN  - 1089-7682
VL  - 29
IS  - 9
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
T1  - Nonlinear phase coupling functions: a numerical study
JF  - Philosophical Transactions of the Royal Society of London, Series A : Mathematical, Physical and Engineering Sciences
N2  - Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here, we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the periodically forced Stuart-Landau oscillator as the paradigmatic model, we determine and numerically analyse the coupling functions up to the fourth order in the force strength. We show that the found nonlinear phase coupling functions can be used for predicting synchronization regions of the forced oscillator.
KW  - phase approximation
KW  - coupling function
KW  - phase response curve
Y1  - 2019
U6  - https://doi.org/10.1098/rsta.2019.0093
SN  - 1364-503X
SN  - 1471-2962
VL  - 377
IS  - 2160
PB  - Royal Society
CY  - London
ER  -