TY  - JOUR
A1  - Kralemann, Björn
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
T1  - Reconstructing phase dynamics of oscillator networks
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - We generalize our recent approach to the reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from a multivariate time series, we first reconstruct genuine phases and then obtain the coupling functions in terms of these phases. Partial norms of these coupling functions quantify directed coupling between oscillators. We illustrate the method by different network motifs for three coupled oscillators and for random networks of five and nine units. We also discuss nonlinear effects in coupling.
Y1  - 2011
U6  - https://doi.org/10.1063/1.3597647
SN  - 1054-1500
VL  - 21
IS  - 2
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Schwabedal, Justus T. C.
A1  - Pikovskij, Arkadij
A1  - Kralemann, Björn
A1  - Rosenblum, Michael
T1  - Optimal phase description of chaotic oscillators
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones. On chaotic attractors possessing a general phase description, we define the optimal isophases as Poincare surfaces showing return times as constant as possible. The dynamics of the resultant optimal phase is maximally decoupled from the amplitude dynamics and provides a proper description of the phase response of chaotic oscillations. The method is illustrated with the Rossler and Lorenz systems.
Y1  - 2012
U6  - https://doi.org/10.1103/PhysRevE.85.026216
SN  - 1539-3755
VL  - 85
IS  - 2
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Kralemann, Björn
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
T1  - Detecting triplet locking by triplet synchronization indices
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We discuss the effect of triplet synchrony in oscillatory networks. In this state the phases and the frequencies of three coupled oscillators fulfill the conditions of a triplet locking, whereas every pair of systems remains asynchronous. We suggest an easy to compute measure, a triplet synchronization index, which can be used to detect such states from experimental data.
Y1  - 2013
U6  - https://doi.org/10.1103/PhysRevE.87.052904
SN  - 1539-3755
VL  - 87
IS  - 5
PB  - American Physical Society
CY  - College Park
ER  -