E. P. Volokitin, V. M. Cheresiz, “About the whole behavior of trajectories of Darboux systems with cubic nonlinearities”, Sib. Èlektron. Mat. Izv., 2018, Volume 15,Pages <nobr>1463

Differentical equations, dynamical systems and optimal control

About the whole behavior of trajectories of Darboux systems with cubic nonlinearities

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

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

Abstract: We study the local and global behavior of trajectories of the 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 with a common factor.

Keywords: polynomial systems, singular points, Poincaré equator, phase portraits.

UDC: 517.925

MSC: 34С05

Received October 10, 2018, published November 23, 2018

DOI: 10.33048/semi.2018.15.120