@book{FreudeKuznetsovPikovskij2006,
  author    = {Freude, Ulrike and Kuznetsov, Sergey P. and Pikovskij, Arkadij},
  title     = {Strange nonchaotic attractors : dynamics between order and chaos in Quasiperiodically Forced Systems},
  publisher = {World Scientific},
  address   = {Singapore},
  isbn      = {981-256633-3},
  pages     = {350 S.},
  year      = {2006},
  language  = {en}
}
@article{KuznetsovFeudelPikovskij1998,
  author    = {Kuznetsov, Sergey P. and Feudel, Ulrike and Pikovskij, Arkadij},
  title     = {Renormalization group for scaling at the torus-doubling terminal point},
  year      = {1998},
  abstract  = {The quasiperiodically forced logistic map is analyzed at the terminal point of the torus-doubling bifurcation curve, where the dynamical regimes of torus, doubled torus, strange nonchaotic attractor, and chaos meet. Using the renormalization group approach we reveal scaling properties both for the critical attractor and for the parameter plane topography near the critical point.},
  language  = {en}
}
@article{Kuznetsov2011,
  author    = {Kuznetsov, Sergey P.},
  title     = {Plykin type attractor in electronic device simulated in MULTISIM},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {21},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {4},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.3646903},
  pages     = {8},
  year      = {2011},
  abstract  = {An electronic device is suggested representing a non-autonomous dynamical system with hyperbolic chaotic attractor of Plykin type in the stroboscopic map, and the results of its simulation with software package NI MULTISIM are considered in comparison with numerical integration of the underlying differential equations. A main practical advantage of electronic devices of this kind is their structural stability that means insensitivity of the chaotic dynamics in respect to variations of functions and parameters of elements constituting the system as well as to interferences and noises.},
  language  = {en}
}
@article{Kuznetsov2016,
  author    = {Kuznetsov, Sergey P.},
  title     = {Parametric chaos generator operating on a varactor diode with the instability limitation decay mechanism},
  series = {Technical Physics},
  volume    = {61},
  journal   = {Technical Physics},
  publisher = {Pleiades Publ.},
  address   = {New York},
  issn      = {1063-7842},
  doi       = {10.1134/S1063784216030129},
  pages     = {436 -- 445},
  year      = {2016},
  abstract  = {Equations are derived for a parametric chaos generator containing three oscillatory circuits and a variable-capacitance diode (varactor) and are reduced to equations for slow amplitudes of parametrically interacting modes. With allowance for quadratic nonlinearity, the problem is reduced to a system of three first-order differential equations for Pikovsky-Rabinovich-Trakhtengerts real amplitudes with a Lorenz-type attractor. In a more accurate description of nonlinearity of the varactor, the equations for slow amplitudes are complex-valued, which leads to the loss of robustness of chaotic dynamics, which is typical of the Lorenz attractor. The results of numerical calculations (portraits of attractors and Lyapunov exponents) in models with different approximation levels are compared.},
  language  = {en}
}
@article{KuznetsovPikovskijBezruckoetal.1997,
  author    = {Kuznetsov, Sergey P. and Pikovskij, Arkadij and Bezrucko, B. P. and Seleznev, E. P. and Feudel, Ulrike},
  title     = {O dinamike nelinejnych sistem po vne¬nim kvaziperiodi\Seskim vozdejstviem vblizi to\Ski okon\Sanija linii bifurkatcii udvoenija tora},
  year      = {1997},
  language  = {de}
}
@article{KuptsovKuznetsovPikovskij2012,
  author    = {Kuptsov, Pavel V. and Kuznetsov, Sergey P. and Pikovskij, Arkadij},
  title     = {Hyperbolic chaos of turing patterns},
  series = {Physical review letters},
  volume    = {108},
  journal   = {Physical review letters},
  number    = {19},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.108.194101},
  pages     = {4},
  year      = {2012},
  abstract  = {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.},
  language  = {en}
}
@article{IsaevaKuznetsovKuznetsov2013,
  author    = {Isaeva, Olga B. and Kuznetsov, Alexey S. and Kuznetsov, Sergey P.},
  title     = {Hyperbolic chaos of standing wave patterns generated parametrically by a modulated pump source},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {87},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {4},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.87.040901},
  pages     = {4},
  year      = {2013},
  abstract  = {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},
  language  = {en}
}
@article{KuptsovKuznetsovPikovskij2013,
  author    = {Kuptsov, Pavel V. and Kuznetsov, Sergey P. and Pikovskij, Arkadij},
  title     = {Hyperbolic chaos at blinking coupling of noisy oscillators},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {87},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {3},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.87.032912},
  pages     = {7},
  year      = {2013},
  abstract  = {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},
  language  = {en}
}
@article{KuznetsovNeumannPikovskijetal.2000,
  author    = {Kuznetsov, Sergey P. and Neumann, Eireen and Pikovskij, Arkadij and Sataev, I. G.},
  title     = {Critical point of tori collision in quasiperiodically forced systems},
  year      = {2000},
  abstract  = {We report on a type of scaling behavior in quasiperiodically forced systems. On the parameter plane the critical point appears as a terminal point of the tori-collision bifurcation curve; its location is found numerically with high precision for two basic models, the forced supercritical circle map and the forced quadratic map. The hypothesis of universality, based on renormalization group arguments, is advanced to explain the observed scaling properties for the critical attractor and for the parameter plane arrangement in the neighborhood of the criticality.},
  language  = {en}
}
@article{KruglovKuznetsovPikovskij2014,
  author    = {Kruglov, Vyacheslav P. and Kuznetsov, Sergey P. and Pikovskij, Arkadij},
  title     = {Attractor of Smale - Williams type in an autonomous distributed system},
  series = {Regular and chaotic dynamics : international scientific journal},
  volume    = {19},
  journal   = {Regular and chaotic dynamics : international scientific journal},
  number    = {4},
  publisher = {Pleiades Publ.},
  address   = {New York},
  issn      = {1560-3547},
  doi       = {10.1134/S1560354714040042},
  pages     = {483 -- 494},
  year      = {2014},
  abstract  = {We consider an autonomous system of partial differential equations for a one-dimensional distributed medium with periodic boundary conditions. Dynamics in time consists of alternating birth and death of patterns with spatial phases transformed from one stage of activity to another by the doubly expanding circle map. So, the attractor in the Poincar, section is uniformly hyperbolic, a kind of Smale - Williams solenoid. Finite-dimensional models are derived as ordinary differential equations for amplitudes of spatial Fourier modes (the 5D and 7D models). Correspondence of the reduced models to the original system is demonstrated numerically. Computational verification of the hyperbolicity criterion is performed for the reduced models: the distribution of angles of intersection for stable and unstable manifolds on the attractor is separated from zero, i.e., the touches are excluded. The example considered gives a partial justification for the old hopes that the chaotic behavior of autonomous distributed systems may be associated with uniformly hyperbolic attractors.},
  language  = {en}
}
@article{IsaevaKuznetsovSataev2012,
  author    = {Isaeva, Olga B. and Kuznetsov, Sergey P. and Sataev, Igor R.},
  title     = {A "saddle-node" bifurcation scenario for birth or destruction of a Smale-Williams solenoid},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {22},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {4},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.4766590},
  pages     = {7},
  year      = {2012},
  abstract  = {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.},
  language  = {en}
}