TY  - JOUR
A1  - Baibolatov, Yernur
A1  - Rosenblum, Michael
A1  - Zhanabaev, Zeinulla Zh.
A1  - Pikovskij, Arkadij
T1  - Complex dynamics of an oscillator ensemble with uniformly distributed natural frequencies and global nonlinear coupling
N2  - We consider large populations of phase oscillators with global nonlinear coupling. For identical oscillators such populations are known to demonstrate a transition from completely synchronized state to the state of self-organized quasiperiodicity. In this state phases of all units differ, yet the population is not completely incoherent but produces a nonzero mean field; the frequency of the latter differs from the frequency of individual units. Here we analyze the dynamics of such populations in case of uniformly distributed natural frequencies. We demonstrate numerically and describe theoretically (i) states of complete synchrony, (ii) regimes with coexistence of a synchronous cluster and a drifting subpopulation, and (iii) self-organized quasiperiodic states with nonzero mean field and all oscillators drifting with respect to it. We analyze transitions between different states with the increase of the coupling strength; in particular we show that the mean field arises via a discontinuous transition. For a further illustration we compare the results for the nonlinear model with those for the Kuramoto-Sakaguchi model.
Y1  - 2010
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.82.016212
SN  - 1539-3755
ER  - 
TY  - JOUR
A1  - Bordyugov, Grigory
A1  - Pikovskij, Arkadij
A1  - Rosenblum, Michael
T1  - Self-emerging and turbulent chimeras in oscillator chains
N2  - We report on a self-emerging chimera state in a homogeneous chain of nonlocally and nonlinearly coupled oscillators. This chimera, i.e., a state with coexisting regions of complete and partial synchrony, emerges via a supercritical bifurcation from a homogeneous state. We develop a theory of chimera based on the Ott-Antonsen equations for the local complex order parameter. Applying a numerical linear stability analysis, we also describe the instability of the chimera and transition to phase turbulence with persistent patches of synchrony.
Y1  - 2010
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.82.035205
SN  - 1539-3755
ER  - 
TY  - JOUR
A1  - Schwabedal, Justus T. C.
A1  - Pikovskij, Arkadij
T1  - Effective phase description of noise-perturbed and noise-induced oscillations
N2  - An effective dynamical description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by the stochastic phase oscillators invariant probability density or its first passage times. Using the first approach the effective phase exhibits the correct frequency and invariant distribution density, whereas the second approach models the proper phase resetting curve. The discrepancy of the effective models is most pronounced for noise-induced oscillations and is related to non-monotonicity of the stochastic phase variable due to fluctuations.
Y1  - 2010
U6  - https://doi.org/10.1140/epjst/e2010-01271-6
SN  - 1951-6355
ER  - 
TY  - JOUR
A1  - Schwabedal, Justus T. C.
A1  - Pikovskij, Arkadij
T1  - Effective phase dynamics of noise-induced oscillations in excitable systems
N2  - We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations.
Y1  - 2010
UR  - http://link.aps.org/doi/10.1103/PhysRevE.81.046218
U6  - https://doi.org/10.1103/Physreve.81.046218
SN  - 1539-3755
ER  -