Three-Dimensional Torus Breakdown and Chaos With Two Zero Lyapunov Exponents in Coupled Radio-Physical GeneratorsSource: Journal of Computational and Nonlinear Dynamics:;2020:;volume( 015 ):;issue: 011::page 0111001-1Author:Stankevich, Nataliya V.
,
Shchegoleva, Natalya A.
,
Sataev, Igor R.
,
Kuznetsov, Alexander P.
DOI: 10.1115/1.4048025Publisher: The American Society of Mechanical Engineers (ASME)
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 Poincaré section, we have shown destruction of three-frequency torus.
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| contributor author | Stankevich, Nataliya V. | |
| contributor author | Shchegoleva, Natalya A. | |
| contributor author | Sataev, Igor R. | |
| contributor author | Kuznetsov, Alexander P. | |
| date accessioned | 2022-02-04T21:55:16Z | |
| date available | 2022-02-04T21:55:16Z | |
| date copyright | 8/26/2020 12:00:00 AM | |
| date issued | 2020 | |
| identifier issn | 1555-1415 | |
| identifier other | cnd_015_12_121002.pdf | |
| identifier uri | http://yetl.yabesh.ir/yetl1/handle/yetl/4274535 | |
| description 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 Poincaré section, we have shown destruction of three-frequency torus. | |
| publisher | The American Society of Mechanical Engineers (ASME) | |
| title | Three-Dimensional Torus Breakdown and Chaos With Two Zero Lyapunov Exponents in Coupled Radio-Physical Generators | |
| type | Journal Paper | |
| journal volume | 15 | |
| journal issue | 11 | |
| journal title | Journal of Computational and Nonlinear Dynamics | |
| identifier doi | 10.1115/1.4048025 | |
| journal fristpage | 0111001-1 | |
| journal lastpage | 0111001-12 | |
| page | 12 | |
| tree | Journal of Computational and Nonlinear Dynamics:;2020:;volume( 015 ):;issue: 011 | |
| contenttype | Fulltext |