TY  - JOUR
A1  - Kuptsov, Pavel V.
A1  - Kuznetsov, Sergey P.
A1  - Pikovskij, Arkadij
T1  - Hyperbolic chaos at blinking coupling of noisy oscillators
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We study an ensemble of identical noisy phase oscillators with a blinking mean-field coupling, where onecluster and two-cluster synchronous states alternate. In the thermodynamic limit the population is described by a nonlinear Fokker-Planck equation. We show that the dynamics of the order parameters demonstrates hyperbolic chaos. The chaoticity manifests itself in phases of the complex mean field, which obey a strongly chaotic Bernoulli map. Hyperbolicity is confirmed by numerical tests based on the calculations of relevant invariant Lyapunov vectors and Lyapunov exponents. We show how the chaotic dynamics of the phases is slightly smeared by finite-size fluctuations. DOI: 10.1103/PhysRevE.87.032912
Y1  - 2013
U6  - https://doi.org/10.1103/PhysRevE.87.032912
SN  - 1539-3755
VL  - 87
IS  - 3
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Isaeva, Olga B.
A1  - Kuznetsov, Alexey S.
A1  - Kuznetsov, Sergey P.
T1  - Hyperbolic chaos of standing wave patterns generated parametrically by a modulated pump source
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We outline a possibility of hyperbolic chaotic dynamics associated with the expanding circle map for spatial phases of parametrically excited standing wave patterns. The model system is governed by a one-dimensional wave equation with nonlinear dissipation. The phenomenon arises due to the pump modulation providing the alternating excitation of modes with the ratio of characteristic scales 1 : 3. DOI: 10.1103/PhysRevE.87.040901
Y1  - 2013
U6  - https://doi.org/10.1103/PhysRevE.87.040901
SN  - 1539-3755
VL  - 87
IS  - 4
PB  - American Physical Society
CY  - College Park
ER  -