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ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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Dynamics of Three Coupled Generators of Quasi-periodic Oscillations

Author(s):

Alexander Petrovich Kuznetsov

Leading Researcher
Kotelnikov Institute of Radio-Engineering and Electronics of RAS, Saratov Branch

apkuz@rambler.ru

Yuliya Viktorovna Sedova

Senior Researcher
Kotelnikov Institute of Radio-Engineering and Electronics of RAS, Saratov Branch

sedovayv@yandex.ru

Nataliya Vladimirovna Stankevich

Senior Researcher
National Research University "Higher School of Economics",

stankevichnv@mail.ru

Abstract:

The dynamics of three coupled generators capable of demonstrating autonomous quasi-periodic oscillations is studied. The complex structure of the Lyapunov charts of the system is discussed, which reveals invariant tori of different dimensions, quasi-periodic bifurcations of tori, and Arnold’s resonant web based on tori of different dimensions. Cases of different types of tuning of individual generators (periodic oscillations, quasi-periodic oscillations) are considered. A detailed numerical bifurcation analysis of the equilibrium state and limit cycles, which form a complex picture of dynamic regimes, is carried out.Common features and differences compared to the case of three coupled van der Pol oscillators are discussed.

Keywords

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