 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
|
| In English (J. Appl. Math. Mech.): | | 799 |
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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 |
09 February 2009 |
| Link to Fulltext |
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