On the monotonicity of the period function of a quadratic system
On the monotonicity of the period function of a quadratic system
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DOI：
10.3934/dcds.2005.13.795
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发表时间：
2005-05
影响因子：
1.1
通讯作者：
Yulin Zhao
中科院分区：
文献类型：
--
作者：
Yulin Zhao
本文研究了二次系统$ \dot x=- y + x y,\quad \dot y=x + 2 y^2-c x^2, \quad -\infty < c < +\infty.$周期函数的单调性，证明了该系统对于$c=1/2$有两个等时中心，对于$c\in(7/5, 2)$周期函数只有一个临界点。对于所有其他情况，周期函数是单调的。这改善了[1]中的结果。
In this paper, we study the monotonicity of the period function of the quadratic system $ \dot x=- y + x y,\quad \dot y=x + 2 y^2-c x^2, \quad -\infty < c < +\infty.$ We show that this system has two isochronous centers for $c=1/2$, and its period function has only one critical point for $c\in(7/5, 2)$. For all other cases, the period function is monotone. This improves the results in [1].