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

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

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Chaotic Rossler Oscillator with Controlled Stimulus Phase

Author(s):

Alexander Petrovich Kuznetsov

Leading Researcher,Doctor of Physical and Mathematical Sciences, Professor
Kotelnikov Institute of Radio-Engineering and Electronics of RAS, Saratov Branch

apkuz@rambler.ru

Yuliya Viktorovna Sedova

Senior Researcher,Candidate of Physical and Mathematical Sciences
Kotelnikov Institute of Radio-Engineering and Electronics of RAS, Saratov Branch

sedovayv@yandex.ru

Nataliya Vladimirovna Stankevich

Senior Researcher,Candidate of Physical and Mathematical Sciences, Docent
Kotelnikov Institute of Radio-Engineering and Electronics of RAS, Saratov Branch

stankevichnv@mail.ru

Abstract:

The dynamics of the chaotic Rossler with external force the phase of which depends on the state of the system is investigated. The study was carried out with the method of charts of Lyapunov exponents that identify areas of different types of dynamics on the plane frequency - amplitude of the external force. Their transformation is discussed with an increase in the parameter responsible for the dependence of the phase on the dynamical variable. The possibility of quasi-periodic dynamics with the set of Arnold tongues was demonstrated. It is shown that with a strong dependence of the phase on the variable of the oscillator, a picture of regular tongues of periodic regimes embedded into the region of chaotic dynamics is formed. Tongues have a threshold in the value of the amplitude of external force. Inside the tongues there are several period-doubling bifurcations of the limit cycles and quasi-periodic dynamics are possible.

Keywords

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