Regular and Chaotic Dynamics

, Volume 22, Issue 5, pp 551–565 | Cite as

A family of models with blue sky catastrophes of different classes

  • Pavel V. Kuptsov
  • Sergey P. Kuznetsov
  • Nataliya V. Stankevich


A generalized model with bifurcations associated with blue sky catastrophes is introduced. Depending on an integer index m, different kinds of attractors arise, including those associated with quasi-periodic oscillations and with hyperbolic chaos. Verification of the hyperbolicity is provided based on statistical analysis of intersection angles of stable and unstable manifolds.


dynamical system blue sky catastrophe quasi-periodic oscillations hyperbolic chaos Smale–Williams solenoid 

MSC2010 numbers

34C28 34C23 37D20 37E99 37G15 37G35 


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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • Pavel V. Kuptsov
    • 1
  • Sergey P. Kuznetsov
    • 2
  • Nataliya V. Stankevich
    • 1
    • 3
  1. 1.Yuri Gagrin State Technical University of SaratovSaratovRussia
  2. 2.Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov BranchSaratovRussia
  3. 3.University of JyväskyläJyväskyläFinland

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