Twelve limit cycles around a singular point in a planar cubic-degree polynomial system |
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| Institution: | 1. School of Business Administration, Shanghai Finance University, Shanghai 201209, China;2. College of Information Technology, Shanghai Ocean University, Shanghai 201306, China;3. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China;1. School of Mathematics and Computer Science, Fujian Normal University, 350007 Fuzhou, PR China;2. Department of Mathematics, Shanghai Normal University, 200234 Shanghai, PR China;1. Department of Electrical Engineering, Guilin College of Aerospace Technology, Guilin 541002, PR China;2. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541003, PR China;3. School of Mathematical Sciences, Fudan University, Shanghai 200433, PR China;1. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, People’s Republic of China;2. Jiangxi University of Science and Technology, Ganzhou 341000, People’s Republic of China;3. Wuhan Center for Magnetic Resonance, State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, People’s Republic of China |
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| Abstract: | In this paper, we prove the existence of 12 small-amplitude limit cycles around a singular point in a planar cubic-degree polynomial system. Based on two previously developed cubic systems in the literature, which have been proved to exhibit 11 small-amplitude limit cycles, we applied a different method to show 11 limit cycles. Moreover, we show that one of the systems can actually have 12 small-amplitude limit cycles around a singular point. This is the best result so far obtained in cubic planar vector fields around a singular point. |
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| Keywords: | Hilbert’s 16th problem Cubic planar system Center Limit cycle Bifurcation Focus value |
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