Three-Dimensional Torus Breakdown and Chaos With Two Zero Lyapunov Exponents in Coupled Radio-Physical Generators-Reference-Cited by-同舟云学术

Three-Dimensional Torus Breakdown and Chaos With Two Zero Lyapunov Exponents in Coupled Radio-Physical Generators

Published:2020-08-26 Issue:11 Volume:15 Page:
ISSN:1555-1415
Container-title:Journal of Computational and Nonlinear Dynamics
language:en
Short-container-title:

Author:

Stankevich Nataliya V.¹,Shchegoleva Natalya A.²,Sataev Igor R.³,Kuznetsov Alexander P.³

Affiliation:

1. Laboratory of Topology Methods in Dynamics,National Research University Higher School of Economics, Nizhny Novgorod 603155, Russia; Department of Radio-Electronics and Telecommunications, Yuri Gagarin State Technical University of Saratov, Saratov 410054, Russia; Department of Applied Cybernetics,St. Petersburg State University, Saint-Peterburg 198504, Russia

2. Department of Radio-Electronics and Telecommunications, Yuri Gagarin State Technical University of Saratov, Saratov 410054, Russia

3. Laboratory of Theoretical Nonlinear Dynamics, Saratov Branch, Kotel'nikov's Institute of Radio-Engineering and Electronics of RAS, Saratov 410019, Russia

Abstract

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.

Funder

Grant of the President of the Russian Federation

Russian Foundation of Basic Research

Publisher

ASME International

Subject

Applied Mathematics,Mechanical Engineering,Control and Systems Engineering,Applied Mathematics,Mechanical Engineering,Control and Systems Engineering

Link

http://asmedigitalcollection.asme.org/computationalnonlinear/article-pdf/doi/10.1115/1.4048025/6560027/cnd_015_11_111001.pdf

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