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| Bifurcations of Limit Cycles Forming Compound Eyes in the Cubic System |
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Citation： |
Li Jibin,Huang Qiming.Bifurcations of Limit Cycles Forming Compound Eyes in the Cubic System[J].Chinese Annals of Mathematics B,1987,8(4):391~403 |
| Page view： 865
Net amount： 932 |
Authors： |
Li Jibin; Huang Qiming |
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| Abstract： |
Let H(n) be the maximal number of limit cycle of planar real polynomial differential system with the degree n and C_m^k denote the nest of k limit cycles enclosing m singular points.By computing detection functions, tne authors study bifurcation and phase diagrams in the class of a planar cubic disturbed Hamiltonian system.In particular, the following conclusion is reached: The planar cubic system(E_3) has 11 limit cycles, which form the pattern of compound eyes of C^1_9\supseteqq 2[C'_3\supseteqq (2C^2_1)] and have the symmetrical structure; so the Hilbert number H(3)\geq 11. |
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