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Limit cycles of quadratic systems

✍ Scribed by Valery A. Gaiko

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
266 KB
Volume
69
Category
Article
ISSN
0362-546X

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✦ Synopsis

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.

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