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

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

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Straight-line Isoclines of Autonomous Planar Cubic Differential Systems and Related Questions

Author(s):

Vyacheslav Beslanovitch Tlyachev

Professor
Engineering Physics Faculty,
Adyghe State University
385000, Pervomayskaya St.,208.
Maykop, Russia

stvb2006@rambler.ru

Adam Damirovitch Ushho

Phd in physics and mathematics
Engineering Physics Faculty,
Adyghe State University
385000, Pervomayskaya St.,208.
Maykop, Russia

uschho76@rambler.ru

Damir Salichovitch Ushho

Associate professor,
Phd in physics and mathematics
The Faculty of Mathematics and Computer Sciences,
Adyghe State University
385000, Pervomayskaya St.,208.
Maykop, Russia

damirubych@mail.ru

Abstract:

The questions related to straight-line isoclines of autonomous differential system with the third order polynomial right-hand side are studied. For this system with the maximum number of parallel between themselves straight-line isoclines the estimation of an upper bound on the general number of straight-line isoclines is given. Moreover the estimation of an upper bound on the number of invariant straight lines of cubic system with at least one equilibrium state and five parallel straight-line isoclines between themselves are obtained. Sufficient conditions of absence of limit cycles in the system with three invariant straight lines and the maximum number of parallel between themselves straight-line isoclines are considered.

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