TY  - JOUR
A1  - Omelʹchenko, Oleh E.
T1  - Nonstationary coherence-incoherence patterns in nonlocally coupled heterogeneous phase oscillators
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - We consider a large ring of nonlocally coupled phase oscillators and show that apart from stationary chimera states, this system also supports nonstationary coherence-incoherence patterns (CIPs). For identical oscillators, these CIPs behave as breathing chimera states and are found in a relatively small parameter region only. It turns out that the stability region of these states enlarges dramatically if a certain amount of spatially uniform heterogeneity (e.g., Lorentzian distribution of natural frequencies) is introduced in the system. In this case, nonstationary CIPs can be studied as stable quasiperiodic solutions of a corresponding mean-field equation, formally describing the infinite system limit. Carrying out direct numerical simulations of the mean-field equation, we find different types of nonstationary CIPs with pulsing and/or alternating chimera-like behavior. Moreover, we reveal a complex bifurcation scenario underlying the transformation of these CIPs into each other. These theoretical predictions are confirmed by numerical simulations of the original coupled oscillator system.
KW  - chimera states
KW  - synchronization
KW  - networks
KW  - Kuramoto
KW  - populations
KW  - dynamics
KW  - bumps
KW  - model
Y1  - 2020
U6  - https://doi.org/10.1063/1.5145259
SN  - 1054-1500
SN  - 1089-7682
VL  - 30
IS  - 4
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Munyaev, Vyacheslav O.
A1  - Smirnov, Lev A.
A1  - Kostin, Vasily A.
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
T1  - Analytical approach to synchronous states of globally coupled noisy rotators
JF  - New journal of physics : the open-access journal for physics
N2  - We study populations of globally coupled noisy rotators (oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous state with constant order parameter for weakly inertial rotators, including the case of zero inertia, when the model is reduced to the Kuramoto model of coupled noise oscillators. These approaches provide also analytical criteria distinguishing supercritical and subcritical transitions to the desynchronized state and indicate the universality of such transitions in rotator ensembles. All the obtained analytical results are confirmed by the numerical ones, both by direct simulations of the large ensembles and by solution of the associated Fokker-Planck equation. We also propose generalizations of the developed approaches for setups where different rotators parameters (natural frequencies, masses, noise intensities, strengths and phase shifts in coupling) are dispersed.
KW  - coupled rotators
KW  - synchronization transition
KW  - hysteresis
KW  - Kuramoto
KW  - model
KW  - noisy systems
Y1  - 2020
U6  - https://doi.org/10.1088/1367-2630/ab6f93
SN  - 1367-2630
VL  - 22
IS  - 2
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -