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IssuesArchive of Issues2010-2pp.135-143

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G.A. Leonov, "A criterion for the existence of four limit cycles in quadratic systems," J. Appl. Math. Mech. 74 (2), 135-143 (2010)
Year 2010 Volume 74 Issue 2 Pages 135-143
Title A criterion for the existence of four limit cycles in quadratic systems
Author(s) G.A. Leonov (St. Petersburg, Russia, leonov@math.spbu.ru)
Abstract A method for the asymptotic integration of the trajectories is proposed for the Liénard equation. The results obtained by this method are used to prove the existence of two "large" limit cycles in quadratic systems with a weak focus. The application of standard procedures of small perturbations of the parameters of quadratic systems enables one to find additionally two "small" limit cycles. It is shown that the criterion obtained for the existence of four limit cycles generalizes the well known Shi theorem.
Received 9 February 2009
Link to Fulltext http://www.sciencedirect.com/science/journal/00218928
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