Pavel V. Kuptsov, Sergey P. Kuznetsov, Nataliya V. Stankevich, “A Family of Models with Blue Sky Catastrophes of Different Classes”, Regul. Chaotic Dyn., 2017, Volume 22, Issue 5,Pages <nobr>551

This article is cited in 4 papers

A Family of Models with Blue Sky Catastrophes of Different Classes

Pavel V. Kuptsov^a, Sergey P. Kuznetsov^b, Nataliya V. Stankevich^ac

^a Yuri Gagrin State Technical University of Saratov, ul. Politehnicheskaya 77, Saratov, 410054 Russia
^b Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, ul. Zelenaya 38, Saratov, 410019 Russia
^c University of Jyväskylä, Mattilanniemi 2, FIN-40014, Finland

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.

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

Received: 17.08.2017
Accepted: 08.09.2017

Language: English

DOI: 10.1134/S1560354717050069