Cascade of torus birth bifurcations and inverse cascade of Shilnikov attractors merging at the threshold of hyperchaos

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Cascade of torus birth bifurcations and inverse cascade of Shilnikov attractors merging at the threshold of hyperchaos. / Sataev, I. R.; Stankevich, N. V.

In: Chaos, Vol. 31, No. 2, 023140, 01.02.2021.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{254242fec1d4427ea3973759550d743b,

title = "Cascade of torus birth bifurcations and inverse cascade of Shilnikov attractors merging at the threshold of hyperchaos",

abstract = "We study the hyperchaos formation scenario in the modified Anishchenko-Astakhov generator. The scenario is connected with the existence of sequence of secondary torus bifurcations of resonant cycles preceding the hyperchaos emergence. This bifurcation cascade leads to the birth of the hierarchy of saddle-focus cycles with a two-dimensional unstable manifold as well as of saddle hyperchaotic sets resulting from the period-doubling cascades of unstable resonant cycles. Hyperchaos is born as a result of an inverse cascade of bifurcations of the emergence of discrete spiral Shilnikov attractors, accompanied by absorbing the cycles constituting this hierarchy.",

author = "Sataev, {I. R.} and Stankevich, {N. V.}",

note = "Publisher Copyright: {\textcopyright} 2021 Author(s).",

year = "2021",

month = feb,

day = "1",

doi = "10.1063/5.0038878",

language = "English",

volume = "31",

journal = "Chaos",

issn = "1054-1500",

publisher = "American Institute of Physics",

number = "2",

}

RIS

TY - JOUR

T1 - Cascade of torus birth bifurcations and inverse cascade of Shilnikov attractors merging at the threshold of hyperchaos

AU - Sataev, I. R.

AU - Stankevich, N. V.

PY - 2021/2/1

Y1 - 2021/2/1

N2 - We study the hyperchaos formation scenario in the modified Anishchenko-Astakhov generator. The scenario is connected with the existence of sequence of secondary torus bifurcations of resonant cycles preceding the hyperchaos emergence. This bifurcation cascade leads to the birth of the hierarchy of saddle-focus cycles with a two-dimensional unstable manifold as well as of saddle hyperchaotic sets resulting from the period-doubling cascades of unstable resonant cycles. Hyperchaos is born as a result of an inverse cascade of bifurcations of the emergence of discrete spiral Shilnikov attractors, accompanied by absorbing the cycles constituting this hierarchy.

AB - We study the hyperchaos formation scenario in the modified Anishchenko-Astakhov generator. The scenario is connected with the existence of sequence of secondary torus bifurcations of resonant cycles preceding the hyperchaos emergence. This bifurcation cascade leads to the birth of the hierarchy of saddle-focus cycles with a two-dimensional unstable manifold as well as of saddle hyperchaotic sets resulting from the period-doubling cascades of unstable resonant cycles. Hyperchaos is born as a result of an inverse cascade of bifurcations of the emergence of discrete spiral Shilnikov attractors, accompanied by absorbing the cycles constituting this hierarchy.

UR - http://www.scopus.com/inward/record.url?scp=85101513377&partnerID=8YFLogxK

U2 - 10.1063/5.0038878

DO - 10.1063/5.0038878

M3 - Article

C2 - 33653044

AN - SCOPUS:85101513377

VL - 31

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 2

M1 - 023140

ER -

ID: 86486972