S. P. Kuznetsov, “Example of blue sky catastrophe accompanied by a birth of Smale–Williams attractor”, Regul. Chaotic Dyn., 15:2-3 (2010), 348

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Regular and Chaotic Dynamics, 2010, Volume 15, Issue 2-3, Pages 348–353 (Mi rcd500)

This article is cited in 10 scientific papers (total in 10 papers)

On the 75th birthday of Professor L.P. Shilnikov

Example of blue sky catastrophe accompanied by a birth of Smale–Williams attractor

S. P. Kuznetsov^ab

^a Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, Germany
^b Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya str., 38, Saratov, 410019, Russia

Citations (10)

Abstract: A model system is proposed, which manifests a blue sky catastrophe giving rise to a hyperbolic attractor of Smale–Williams type in accordance with theory of Shilnikov and Turaev. Some essential features of the transition are demonstrated in computations, including Bernoulli-type discrete-step evolution of the angular variable, inverse square root dependence of the first return time on the bifurcation parameter, certain type of dependence of Lyapunov exponents on control parameter for the differential equations and for the Poincaré map.

Keywords: attractor, bifurcation, Smale–Williams solenoid, Lyapunov exponent.

Received: 24.02.2010
Accepted: 03.03.2010

Document Type: Personalia

MSC: 34C28, 34C23, 37D20, 37E99, 37G15, 37G35

Language: English

Citation: S. P. Kuznetsov, “Example of blue sky catastrophe accompanied by a birth of Smale–Williams attractor”, Regul. Chaotic Dyn., 15:2-3 (2010), 348–353

Citation in format AMSBIB

\Bibitem{Kuz10}

\by S. P. Kuznetsov

\paper Example of blue sky catastrophe accompanied by a birth of Smale–Williams attractor

\jour Regul. Chaotic Dyn.

\yr 2010

\vol 15

\issue 2-3

\pages 348--353

\mathnet{http://mi.mathnet.ru/rcd500}

Linking options:

https://www.mathnet.ru/eng/rcd500

https://www.mathnet.ru/eng/rcd/v15/i2/p348

This publication is cited in the following 10 articles:

Kruglov V.P. Kuptsov V P., “Theoretical Models of Physical Systems With Rough Chaos”, Izv. Vyss. Uchebn. Zaved.-Prikl. Nelineynaya Din., 29:1 (2021), 35–77
V. M. Doroshenko, V. P. Kruglov, S. P. Kuznetsov, “Smale – Williams Solenoids in a System of Coupled Bonhoeffer – van der Pol Oscillators”, Nelin. Dinam., 14:4 (2018), 435–451
Pavel V. Kuptsov, Sergey P. Kuznetsov, Nataliya V. Stankevich, “A Family of Models with Blue Sky Catastrophes of Different Classes”, Regul. Chaotic Dyn., 22:5 (2017), 551–565
V. M. Doroshenko, V. P. Kruglov, S. P. Kuznetsov, “Generator khaosa s attraktorom Smeila–Vilyamsa na osnove effekta gibeli kolebanii”, Nelineinaya dinam., 13:3 (2017), 303–315
Sergey P. Kuznetsov, Vyacheslav P. Kruglov, “Verification of Hyperbolicity for Attractors of Some Mechanical Systems with Chaotic Dynamics”, Regul. Chaotic Dyn., 21:2 (2016), 160–174
A. Yu. Zhalnin, “Ot kvazigarmonicheskikh ostsillyatsii k neironnym spaikam i berstam: raznoobrazie rezhimov giperbolicheskogo khaosa na osnove attraktora Smeila – Vilyamsa”, Nelineinaya dinam., 12:1 (2016), 53–73
S. P. Kuznetsov, “Giperbolicheskii khaos v avtokolebatelnykh sistemakh na osnove troinogo sharnirnogo mekhanizma: Proverka otsutstviya kasanii ustoichivykh i neustoichivykh mnogoobrazii fazovykh traektorii”, Nelineinaya dinam., 12:1 (2016), 121–143
Sergey P. Kuznetsov, “Hyperbolic Chaos in Self-oscillating Systems Based on Mechanical Triple Linkage: Testing Absence of Tangencies of Stable and Unstable Manifolds for Phase Trajectories”, Regul. Chaotic Dyn., 20:6 (2015), 649–666
Vyacheslav P. Kruglov, Sergey P. Kuznetsov, Arkady Pikovsky, “Attractor of Smale–Williams Type in an Autonomous Distributed System”, Regul. Chaotic Dyn., 19:4 (2014), 483–494
S. P. Kuznetsov, “Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics”, Phys. Usp., 54:2 (2011), 119–144

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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