LIMIT CYCLE PROBLEM OF QUADRATIC SYSTEM OF TYPE ( Ⅲ )m=0, ( Ⅲ ) |
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作者姓名: | Ali. Elamin. M. Saeed Luo Dingjun |
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作者单位: | College of Math. and Comput. Sei. , Nanjing Normal Univ. , Nanjing 210097,China. |
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基金项目: | Project supported by the National Natural Science Foundation of China (10471066). |
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摘 要: | To continue the discussion in (Ⅰ ) and ( Ⅱ ),and finish the study of the limit cycle problem for quadratic system ( Ⅲ )m=0 in this paper. Since there is at most one limit cycle that may be created from critical point O by Hopf bifurcation,the number of limit cycles depends on the different situations of separatrix cycle to be formed around O. If it is a homoclinic cycle passing through saddle S1 on 1 +ax-y = 0,which has the same stability with the limit cycle created by Hopf bifurcation,then the uniqueness of limit cycles in such cases can be proved. If it is a homoclinic cycle passing through saddle N on x= 0,which has the different stability from the limit cycle created by Hopf bifurcation,then it will be a case of two limit cycles. For the case when the separatrix cycle is a heteroclinic cycle passing through two saddles at infinity,the discussion of the paper shows that the number of limit cycles will change from one to two depending on the different values of parameters of system.
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关 键 词: | 二次方程系统 有限循环问题 异循环 Hopf分歧 临界点 |
收稿时间: | 2004-11-08 |
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