The generalized four-dimensional Rössler system is studied. Main bifurcation scenarios leading to a hyperchaos are described phenomenologically and their implementation in the model is demonstrated. In particular, we show that the formation of hyperchaotic invariant sets is related mainly to cascades (finite or infinite) of nondegenerate bifurcations of two types: period-doubling bifurcations of saddle cycles with a one-dimensional unstable invariant manifold and Neimark-Sacker bifurcations of stable cycles. The onset of the discrete hyperchaotic Shilnikov attractors containing a saddle-focus cycle with a two-dimensional unstable invariant manifold is confirmed numerically in a Poincaré map of the model. A new phenomenon, “jump of hyperchaoticity,” when the attractor under consideration becomes hyperchaotic due to the boundary crisis of some other attractor, is discovered.
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December 2020
Research Article|
December 14 2020
Scenarios of hyperchaos occurrence in 4D Rössler system
Special Collection:
Chaos: From Theory to Applications
N. Stankevich
;
N. Stankevich
a)
1
Laboratory of Topological Methods in Dynamics, National Research University Higher School of Economics
, 25/12 Bolshay Pecherskaya str., Nizhny Novgorod 603155, Russia
a)Author to whom correspondence should be addressed: stankevichnv@mail.ru. Also at: Department of Radio-Electronics and Telecommunications, Yuri Gagarin State Technical University of Saratov, 77 Politekhnicheskaya str., Saratov 410054, Russia and Department of Applied Cybernetics, St. Petersburg State University, Peterhof, 28 Universitetskiy proezd, St. Petersburg 198504, Russia.
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A. Kazakov
;
A. Kazakov
b)
2
International Laboratory of Dynamical Systems and Applications, National Research University Higher School of Economics, 25/12 Bolshaya Pecherskaya str., Nizhny Novgorod 603155
, Russia
3
Scientific and Educational Mathematical Center “Mathematics of Future Technologies”, Lobachevsky State University of Nizhny Novgorod, 23 Prospekt Gagarina, Nizhny Novgorod 603950
, Russia
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S. Gonchenko
S. Gonchenko
c)
2
International Laboratory of Dynamical Systems and Applications, National Research University Higher School of Economics, 25/12 Bolshaya Pecherskaya str., Nizhny Novgorod 603155
, Russia
3
Scientific and Educational Mathematical Center “Mathematics of Future Technologies”, Lobachevsky State University of Nizhny Novgorod, 23 Prospekt Gagarina, Nizhny Novgorod 603950
, Russia
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a)Author to whom correspondence should be addressed: stankevichnv@mail.ru. Also at: Department of Radio-Electronics and Telecommunications, Yuri Gagarin State Technical University of Saratov, 77 Politekhnicheskaya str., Saratov 410054, Russia and Department of Applied Cybernetics, St. Petersburg State University, Peterhof, 28 Universitetskiy proezd, St. Petersburg 198504, Russia.
b)
Electronic mail: kazakovdz@yandex.ru
c)
Electronic mail: sergey.gonchenko@mail.ru
Note: This paper is part of the Focus Issue, Chaos: From Theory to Applications.
Chaos 30, 123129 (2020)
Article history
Received:
August 31 2020
Accepted:
November 19 2020
Connected Content
A correction has been published:
Publisher’s Note: “Scenarios of hyperchaos occurrence in 4D Rössler system” [Chaos 30, 123129 (2020)]
Citation
N. Stankevich, A. Kazakov, S. Gonchenko; Scenarios of hyperchaos occurrence in 4D Rössler system. Chaos 1 December 2020; 30 (12): 123129. https://doi.org/10.1063/5.0027866
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