Global Qualitative Analysis of Kukles and Lienard Cubic Systems
by
Valery A. Gaiko
Belarusian State University of Informatics and Radioelectronics

Two-dimensional polynomial dynamical systems are considered. Using Erugin's two-isocline method, we construct a canonical cubic system of Kukles type and carry out the global analysis of its special case corresponding to a generalized Liénard equation. We prove that the foci of such a Liénard system can be at most of second order and that this particular system can have at least three limit cycles in the whole phase plane. Moreover, unlike all previous works on the Kukles-type systems, we study global bifurcations of limit and separatrix cycles, using arbitrary (including as large as possible) field-rotation parameters of our canonical system. As a result, we have obtained a classification of all possible types of separatrix cycles for this generalized Liénard system and also all possible distributions of its limit cycles, conjecturing that this system has at most three limit cycles.

Date received: March 15, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # canu-62.