|
Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2013, Volume 9, Number 2, Pages 267–294
(Mi nd390)
|
|
|
|
This article is cited in 3 scientific papers (total in 3 papers)
On a bifurcation scenario of a birth of attractor of Smale–Williams type
Olga B. Isaevaab, Sergey P. Kuznetsovabc, Igor R. Sataeva, Arkady Pikovskyc a Saratov Branch of Kotelnikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov, Russia
b Saratov State University, Saratov, Russia
c Institute of Physics and Astronomy, University of Potsdam, Germany, Potsdam-Golm
Abstract:
We describe one possible scenario of destruction or of a birth of the hyperbolic attractors considering the Smale–Williams solenoid as an example. The content of the transition observed under variation of the control parameter is the pairwise merge of the orbits belonging to the attractor and to the unstable invariant set on the border of the basin of attraction, in the course of the set of bifurcations of the saddle-node type. The transition is not a single event, but occupies a finite interval on the control parameter axis. In an extended space of the state variables and the control parameter this scenario can be regarded as a mutual transformation of the stable and unstable solenoids one to each other. Several model systems are discussed manifesting this scenario e.g. the specially designed iterative maps and the physically realizable system of coupled alternately activated non-autonomous van der Pol oscillators. Detailed studies of inherent features and of the related statistical and scaling properties of the scenario are provided.
Keywords:
strange attractor, chaos, bifurcation, self-sustained oscillator, hyperbolic chaos.
Received: 10.01.2013 Revised: 27.02.2013
Citation:
Olga B. Isaeva, Sergey P. Kuznetsov, Igor R. Sataev, Arkady Pikovsky, “On a bifurcation scenario of a birth of attractor of Smale–Williams type”, Nelin. Dinam., 9:2 (2013), 267–294
Linking options:
https://www.mathnet.ru/eng/nd390 https://www.mathnet.ru/eng/nd/v9/i2/p267
|
Statistics & downloads: |
Abstract page: | 403 | Full-text PDF : | 105 | References: | 58 | First page: | 1 |
|