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A criterion for the existence of four limit cycles in quadratic systems |
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| Authors: | G.A. Leonov |
| Affiliation: | 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Department of Mechanics, Shanghai University, Shanghai 200072, China;2. The School of Mechanical Engineering, Zhengzhou University, Zhengzhou, Henan 450001, China;3. Department of Civil Engineering, The University of Akron, OH 44325-3905, USA;1. St. Petersburg State University, Universitetsky pr. 28, St. Petersburg 198504, Russia;2. Harbin Institute of Technology, Xidazhi Street, 92, Harbin 150001, China |
| 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. |
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