Limit cycles of quadratic systems |
| |
Authors: | Valery A Gaiko |
| |
Institution: | aDepartment of Mathematics, Belarusian State University of Informatics and Radioelectronics, L. Beda Street 6-4, Minsk 220040, Belarus |
| |
Abstract: | In this paper, the global qualitative analysis of planar quadratic dynamical systems is established and a new geometric approach to solving Hilbert’s Sixteenth Problem in this special case of polynomial systems is suggested. Using geometric properties of four field rotation parameters of a new canonical system which is constructed in this paper, we present a proof of our earlier conjecture that the maximum number of limit cycles in a quadratic system is equal to four and their only possible distribution is (3:1) V.A. Gaiko, Global Bifurcation Theory and Hilbert’s Sixteenth Problem, Kluwer, Boston, 2003]. Besides, applying the Wintner–Perko termination principle for multiple limit cycles to our canonical system, we prove in a different way that a quadratic system has at most three limit cycles around a singular point (focus) and give another proof of the same conjecture. |
| |
Keywords: | Hilbert’ s sixteenth problem Wintner– Perko termination principle Planar quadratic dynamical system Field rotation parameter Bifurcation Limit cycle Separatrix cycle |
本文献已被 ScienceDirect 等数据库收录! |
|