TY  - JOUR
A1  - Kuptsov, Pavel V.
A1  - Kuznetsov, Sergey P.
A1  - Pikovskij, Arkadij
T1  - Hyperbolic chaos of turing patterns
JF  - Physical review letters
N2  - We consider time evolution of Turing patterns in an extended system governed by an equation of the Swift-Hohenberg type, where due to an external periodic parameter modulation longwave and shortwave patterns with length scales related as 1:3 emerge in succession. We show theoretically and demonstrate numerically that the spatial phases of the patterns, being observed stroboscopically, are governed by an expanding circle map, so that the corresponding chaos of Turing patterns is hyperbolic, associated with a strange attractor of the Smale-Williams solenoid type. This chaos is shown to be robust with respect to variations of parameters and boundary conditions.
Y1  - 2012
U6  - https://doi.org/10.1103/PhysRevLett.108.194101
SN  - 0031-9007
VL  - 108
IS  - 19
PB  - American Physical Society
CY  - College Park
ER  - 
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  -