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Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations |
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| Authors: | Tonghua Zhang Maoan Han Hong Zang Xinzhu Meng |
| Institution: | a Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China b Department of Basic Courses, Shandong University of Science and Technology, Tai'an, Shandong 271019, China |
| Abstract: | This paper is concerned with the number of limit cycles of a cubic system with quartic perturbations. Fifteen limit cycles are found and their distributions are studied by using the methods of bifurcation theory and qualitative analysis. It gives rise to the conclusion: H(4) 15, where H(n) is the Hilbert number for the second part of Hilbert's 16th problem. |
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