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

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

On the Acyclicity of a Cubic Differential System Having Four Invariant Straight Lines and a Unstable Focus


Adam Damirovich Ushho

Adygea State University, Department of Theoretical Physics
Associate Professor, Candidate of Physical and Mathematical Sciences,
208 Pervomayskaya str., Maykop, Russian Federation


The sufficient conditions for the absence of limit cycles in a cubic autonomous differential system having four invariant straight lines and a unstable focus are found. Examples illustrating the provisions of the acyclicity theorem of a cubic system with four invariant straight lines and a unstable focus are given. Examples of cubic differential systems with four invariant lines having a limit cycle located both inside and outside the parallelogram formed by invariant straight lines are considered.



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