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The number and distributions of limit cycles for a class of cubic near-Hamiltonian systems |
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| Authors: | Hong Zang Tonghua Zhang Maoan Han |
| Affiliation: | a Department of Mathematics, Shanghai Jiao Tong University, 200240 Shanghai, PR China b Department of Chemical Engineering, Curtin University of Technology, Perth, Australia c Department of Mathematics, Shanghai Normal University, 200234 Shanghai, PR China |
| Abstract: | This paper concerns with the number of limit cycles for a cubic Hamiltonian system under cubic perturbation. The fact that there exist 9-11 limit cycles is proved. The different distributions of limit cycles are given by using methods of bifurcation theory and qualitative analysis, among which two distributions of eleven limit cycles are new. |
| Keywords: | Homoclinic bifurcation Distribution of limit cycle Hamiltonian system Hilbert's 16th problem |
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