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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
Article

Abstract

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.

Keywords

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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