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

  • L.P. Shilnikov-75
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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.

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Authors and Affiliations

  1. Saratov Branch, Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Zelenaya str., 38, Saratov, 410019, Russia

    S. P. Kuznetsov

  2. Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476, Potsdam-Golm, Germany

    S. P. Kuznetsov

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  1. S. P. Kuznetsov
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Kuznetsov, S.P. Example of blue sky catastrophe accompanied by a birth of Smale-Williams attractor. Regul. Chaot. Dyn. 15, 348–353 (2010). https://doi.org/10.1134/S1560354710020206

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