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A unified quantification of synchrony in globally coupled populations with the Wiener order parameter
Arkady Pikovsky, Michael Rosenblum
We tackle the quantification of synchrony in globally coupled populations. Furthermore, we treat the problem of incomplete observations when the population mean field is unavailabl…
High-order phase reduction for coupled 2D oscillators
Erik T. K. Mau, Michael Rosenblum, Arkady Pikovsky
Phase reduction is a general approach to describe coupled oscillatory units in terms of their phases, assuming that the amplitudes are enslaved. For such a reduction, the coupling…
Optimizing charge-balanced pulse stimulation for desynchronization
Erik T. K. Mau, Michael Rosenblum
Collective synchronization in a large population of self-sustained units appears both in natural and engineered systems. Sometimes this effect is in demand, while in some cases, it…
Two Mechanisms of Remote Synchronization in a Chain of Stuart-Landau Oscillators
Mohit Kumar, Michael Rosenblum
Remote synchronization implies that oscillators interacting not directly but via an additional unit (hub) adjust their frequencies and exhibit frequency locking while the hub remai…
Controlling collective synchrony in oscillatory ensembles by precisely timed pulses
Michael Rosenblum
We present an efficient technique for control of synchrony in a globally coupled ensemble by pulsatile action. We assume that we can observe the collective oscillation and can stim…
Solitary States and Partial Synchrony in Oscillatory Ensembles with Attractive and Repulsive Interactions
Erik Teichmann, Michael Rosenblum
We numerically and analytically analyze transitions between different synchronous states in a network of globally coupled phase oscillators with attractive and repulsive interactio…
Two types of quasiperiodic partial synchrony in oscillator ensembles
Michael Rosenblum, Arkady Pikovsky
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…
Dynamics of weakly inhomogeneous oscillator populations: Perturbation theory on top of Watanabe-Strogatz integrability
Vladimir Vlasov, Michael Rosenblum, Arkady Pikovsky
As has been shown by Watanabe and Strogatz (WS) [Phys. Rev. Lett., 70, 2391 (1993)], a population of identical phase oscillators, sine-coupled to a common field, is a partially int…
Chimera-like states in an ensemble of globally coupled oscillators
Azamat Yeldesbay, Arkady Pikovsky, Michael Rosenblum
We demonstrate emergence of a complex state in a homogeneous ensemble of globally coupled identical oscillators, reminiscent of chimera states in locally coupled oscillator lattice…
Effective phase connectivity from observations
Björn Kralemann, Arkady Pikovsky, Michael Rosenblum
We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series d…
Optimal Phase Description of Chaotic Oscillators
Justus T. C. Schwabedal, Arkady Pikovsky, Björn Kralemann +1
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…
Reconstructing phase dynamics of oscillator networks
Björn Kralemann, Arkady Pikovsky, Michael Rosenblum
We generalize our recent approach to reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E, 77, 066205 (2008)] to cover the case of s…
Collective Phase Chaos in the Dynamics of Interacting Oscillator Ensembles
Sergey P. Kuznetsov, Arkady Pikovsky, Michael Rosenblum
We study chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, wh…