Planar polynomial vector fields having first integrals and algebraic limit cycles |
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| Authors: | Jinlong Cao Haixia Jiang |
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| Institution: | a Financial Engineering Research Center for Shanghai Jiaotong University, Shanghai 200052, PR China
b Key Laboratory of Microbial Metabolism, Ministry of Education, College of Life Sciences and Biotechnology, Shanghai Jiaotong University, Shanghai 200240, PR China |
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| Abstract: | With the help of Abel differential equations we obtain a new class of Darboux integrable planar polynomial differential systems, which have degenerate infinity. Moreover such integrable systems may have algebraic limit cycles. Also we present the explicit expressions of these algebraic limit cycles for quintic systems. |
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| Keywords: | Darboux first integral Algebraic limit cycles |
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