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  - 
TY  - JOUR
A1  - Isaeva, Olga B.
A1  - Kuznetsov, Sergey P.
A1  - Sataev, Igor R.
T1  - A "saddle-node" bifurcation scenario for birth or destruction of a Smale-Williams solenoid
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - Formation or destruction of hyperbolic chaotic attractor under parameter variation is considered with an example represented by Smale-Williams solenoid in stroboscopic Poincare map of two alternately excited non-autonomous van der Pol oscillators. The transition occupies a narrow but finite parameter interval and progresses in such way that periodic orbits constituting a "skeleton" of the attractor undergo saddle-node bifurcation events involving partner orbits from the attractor and from a non-attracting invariant set, which forms together with its stable manifold a basin boundary of the attractor.
Y1  - 2012
U6  - https://doi.org/10.1063/1.4766590
SN  - 1054-1500
VL  - 22
IS  - 4
PB  - American Institute of Physics
CY  - Melville
ER  -