Scenarios of hyperchaos occurrence in 4D Rössler system

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Scenarios of hyperchaos occurrence in 4D Rössler system. / Stankevich, N.; Kazakov, A.; Gonchenko, S.

в: Chaos, Том 30, № 12, 123129, 01.12.2020.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{159028c187594f4fbed9484a6b53e425,

title = "Scenarios of hyperchaos occurrence in 4D R{\"o}ssler system",

abstract = "The generalized four-dimensional R{\"o}ssler 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 Poincar{\'e} 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. ",

author = "N. Stankevich and A. Kazakov and S. Gonchenko",

note = "Publisher Copyright: {\textcopyright} 2020 Author(s).",

year = "2020",

month = dec,

day = "1",

doi = "10.1063/5.0027866",

language = "English",

volume = "30",

journal = "Chaos",

issn = "1054-1500",

publisher = "American Institute of Physics",

number = "12",

}

RIS

TY - JOUR

T1 - Scenarios of hyperchaos occurrence in 4D Rössler system

AU - Stankevich, N.

AU - Kazakov, A.

AU - Gonchenko, S.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85099234105&partnerID=8YFLogxK

U2 - 10.1063/5.0027866

DO - 10.1063/5.0027866

M3 - Article

C2 - 33380035

AN - SCOPUS:85099234105

VL - 30

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 12

M1 - 123129

ER -

ID: 86484367

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