E. P. Volokitin, V. M. Cheresiz, “Algebraic limit cycles of planar cubic systems”, Sib. Èlektron. Mat. Izv., 2020, Volume 17,Pages <nobr>2045

This article is cited in 2 papers

Differentical equations, dynamical systems and optimal control

Algebraic limit cycles of planar cubic systems

E. P. Volokitin^ab, V. M. Cheresiz^a

^a Sobolev Institute of Mathematics 4, Acad. Koptyug ave., Novosibirck, 630090, Russia
^b Novosibirsk State University, 2, Pirogova str., Novosibirck, 630090, Russia

Abstract: We study algebraic limit cycles of differential systems of the form $\dot x= x+P_3(x,y), \ \dot y=y+Q_3(x,y)$ where $P_3(x,y)$ and $Q_3(x,y)$ are homogeneous cubic polynomials.

Keywords: polynomial systems, algebraic limit cycles, non-algebraic limit cycles, phase portraits.

UDC: 517.925

MSC: 34C05

Received October 27, 2020, published December 10, 2020

Language: English

DOI: 10.33048/semi.2020.17.136