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A criterion for the existence of four limit cycles in quadratic systems

✍ Scribed by G.A. Leonov

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
311 KB
Volume
74
Category
Article
ISSN
0021-8928

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✦ Synopsis

A method for the asymptotic integration of the trajectories is proposed for the LiΓ©nard 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.

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