The period function of reversible Lotka-Volterra quadratic centers
The period function of reversible Lotka-Volterra quadratic centers
复制标题
可逆 Lotka-Volterra 二次中心的周期函数
DOI：
10.1016/j.jde.2021.10.060
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发表时间：
2022
影响因子：
2.4
通讯作者：
Wang Decheng
中科院分区：
文献类型：
--
作者：
Li Jinming;Li Chengzhi;Liu Changjian;Wang Decheng
本文证明了可逆Lotka-Volterra二次系统的周期函数是单调的，除非伴随的中心是等距的。对于这类二次系统，传统的关于周期函数单调性的判据函数不起作用，我们将判据函数改进为新的不同形式，使其能适用于系统中不同的参数值。此外，为了克服参数的指数函数出现在第一次积分中的困难，我们将解析表达式与其几何意义和符号计算结合起来，进行了联合收割机的研究。这些方法可以用于其他问题。
In this paper it is proved that the period function of reversible Lotka-Volterra quadratic systems is monotone, unless the associated center is isochronous. For this class of quadratic systems, the traditional criterion function on the monotonicity of period function does not work, we improve the criterion function to new different forms such that it can be used for different values of the parameters in the system. Furthermore, to overcome the difficulty that the exponential function of the parameter appears in the first integral, in our study we combine the analytic expressions with their geometric meanings and symbolic computations. These methods may be used for other problems.