Three-Dimensional torus breakdown and chaos with two zero lyapunov exponents in coupled radio-Physical generators

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Three-Dimensional torus breakdown and chaos with two zero lyapunov exponents in coupled radio-Physical generators. / Stankevich, Nataliya V.; Shchegoleva, Natalya A.; Sataev, Igor R.; Kuznetsov, Alexander P.

In: Journal of Computational and Nonlinear Dynamics, Vol. 15, No. 11, 111001, 11.2020.

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

Author

Stankevich, Nataliya V. ; Shchegoleva, Natalya A. ; Sataev, Igor R. ; Kuznetsov, Alexander P. / Three-Dimensional torus breakdown and chaos with two zero lyapunov exponents in coupled radio-Physical generators. In: Journal of Computational and Nonlinear Dynamics. 2020 ; Vol. 15, No. 11.

BibTeX

@article{4e48b32bc09f4c04b9fee03a3870a301,

title = "Three-Dimensional torus breakdown and chaos with two zero lyapunov exponents in coupled radio-Physical generators",

abstract = "Using an example a system of two coupled generators of quasi-periodic oscillations, we study the occurrence of chaotic dynamics with one positive, two zero, and several negative Lyapunov exponents. It is shown that such dynamic arises as a result of a sequence of bifurcations of two-frequency torus doubling and involves saddle tori occurring at their doublings. This transition is associated with typical structure of parameter plane, like cross-road area and shrimp-shaped structures, based on the two-frequency quasi-periodic dynamics. Using double Poincare section, we have shown destruction of three-frequency torus.",

keywords = "Chaos, Dynamical system, Lyapunov exponents, Multifrequency quasi-periodic oscillations, Torus-doubling bifurcation",

author = "Stankevich, {Nataliya V.} and Shchegoleva, {Natalya A.} and Sataev, {Igor R.} and Kuznetsov, {Alexander P.}",

note = "Publisher Copyright: Copyright {\textcopyright} 2020 by ASME.",

year = "2020",

month = nov,

doi = "10.1115/1.4048025",

language = "English",

volume = "15",

journal = "Journal of Computational and Nonlinear Dynamics",

issn = "1555-1423",

publisher = "American Society of Mechanical Engineers",

number = "11",

}

RIS

TY - JOUR

T1 - Three-Dimensional torus breakdown and chaos with two zero lyapunov exponents in coupled radio-Physical generators

AU - Stankevich, Nataliya V.

AU - Shchegoleva, Natalya A.

AU - Sataev, Igor R.

AU - Kuznetsov, Alexander P.

PY - 2020/11

Y1 - 2020/11

N2 - Using an example a system of two coupled generators of quasi-periodic oscillations, we study the occurrence of chaotic dynamics with one positive, two zero, and several negative Lyapunov exponents. It is shown that such dynamic arises as a result of a sequence of bifurcations of two-frequency torus doubling and involves saddle tori occurring at their doublings. This transition is associated with typical structure of parameter plane, like cross-road area and shrimp-shaped structures, based on the two-frequency quasi-periodic dynamics. Using double Poincare section, we have shown destruction of three-frequency torus.

AB - Using an example a system of two coupled generators of quasi-periodic oscillations, we study the occurrence of chaotic dynamics with one positive, two zero, and several negative Lyapunov exponents. It is shown that such dynamic arises as a result of a sequence of bifurcations of two-frequency torus doubling and involves saddle tori occurring at their doublings. This transition is associated with typical structure of parameter plane, like cross-road area and shrimp-shaped structures, based on the two-frequency quasi-periodic dynamics. Using double Poincare section, we have shown destruction of three-frequency torus.

KW - Chaos

KW - Dynamical system

KW - Lyapunov exponents

KW - Multifrequency quasi-periodic oscillations

KW - Torus-doubling bifurcation

UR - http://www.scopus.com/inward/record.url?scp=85096515438&partnerID=8YFLogxK

U2 - 10.1115/1.4048025

DO - 10.1115/1.4048025

M3 - Article

AN - SCOPUS:85096515438

VL - 15

JO - Journal of Computational and Nonlinear Dynamics

JF - Journal of Computational and Nonlinear Dynamics

SN - 1555-1423

IS - 11

M1 - 111001

ER -

ID: 86483395