Regular and Chaotic Dynamics

, Volume 15, Issue 2–3, pp 348–353 | Cite as

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

  • S. P. KuznetsovEmail author
L.P. Shilnikov-75 Special Issue


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.

Key words

attractor bifurcation Smale-Williams solenoid Lyapunov exponent 

MSC2000 numbers

34C28 34C23 37D20 37E99 37G15 37G35 


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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Saratov BranchKotel’nikov’s Institute of Radio-Engineering and Electronics of RASSaratovRussia
  2. 2.Department of Physics and AstronomyUniversity of PotsdamPotsdam-GolmGermany

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