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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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Visualization of Four Limit Cycles of Two-dimensional Quadratic Systems in the Parameter Space

Author(s):

G. A. Leonov

Professor
Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics
Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia

leonov@math.spbu.ru

Irina G. Burova

Dr. of Science
Mathematics and Mechanics Faculty,
St. Petersburg State University
Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia.

burovaig@mail.ru

Konstantin D. Alexandrov

Mathematics and Mechanics Faculty,
St. Petersburg State University
Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia.

Konstantin.239.Alexandrov@gmail.com

Abstract:

This work is devoted to the visualization of a domain which contains four limit cycles for quadratic dynamic systems of differential equations of the first order with real coefficients. Visualization of the domain is made in three-dimensional space of the coefficients which correspond to nonlinear part of the quadratic system. Theoretical and practical aspects of the numerical solutions of the Cauchy problem for unstable systems are discussed.

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