uniqueness of limit cycles for a class of cubic systems with two invariant straight lines
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ID: 187880
2010
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Abstract
A class of cubic systems with two invariant straight lines dx/dt=y(1-x2), dy/dt=-x+δy+nx2+mxy+ly2+bxy2. is studied. It is obtained that the focal quantities of O(0,0) are, W0=δ; if W0=0, then W1=m(n+l); if W0=W1=0, then W2=−nm(b+1); if W0=W1=W2=0, then O is a center, and it has been proved that the above mentioned cubic system has at most one limit cycle surrounding weak focal O(0,0). This paper also aims to solve the remaining issues in the work of Zheng and Xie (2009).
| Reference Key |
xie2010discreteuniqueness
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|---|---|
| Authors | ;Xiangdong Xie;Fengde Chen;Qingyi Zhan |
| Journal | Journal of the American Heart Association |
| Year | 2010 |
| DOI |
10.1155/2010/737068
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| URL | |
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