In this work we study the criticality of some planar systems of polynomial differential equations having a center for various low degrees $n.$ To this end, we present a method which is equivalent to the use of the first non-identically zero Melnikov function in the problem of limit cycles bifurcation, but adapted to the period function. We prove that the Taylor development of this first order function can be found from the linear terms of the corresponding period constants. Later, we consider families which are isochronous centers being perturbed inside the reversible centers class, and we prove our criticality results by finding the first order Taylor developments of the period constants with respect to the perturbation parameters. In particular, we obtain that at least 22 critical periods bifurcate for $n=6,$ 37 for $n=8,$ 57 for $n=10,$ 80 for $n=12,$ 106 for $n=14,$ and 136 for $n=16.$ Up to our knowledge, these values improve the best current lower bounds.

在这项工作中，我们研究了以低度为中心的多项式微分方程平面系统的临界性 $ñ。$为此，我们提出了一种方法，该方法等效于在极限环分叉问题中使用第一个非相同零梅尔尼科夫函数，但适用于周期函数。我们证明可以从相应周期常数的线性项中找到此一阶函数的泰勒展开式。后来，我们考虑到等时中心的家庭在可逆中心类中受到扰动，并且我们通过找到相对于扰动参数的周期常数的一阶泰勒展开来证明我们的临界结果。特别是，我们获得了至少22个关键时期$ñ=6，$ 37为 $ñ=8，$ 57为 $ñ=10，$ 80为 $ñ=12，$ 106为 $ñ=14，$ 和136为 $ñ=16。$ 据我们所知，这些值改善了最佳的电流下限。