相图
数学
中心(范畴论)
五次函数
分叉
锂é纳德方程
数学分析
订单(交换)
班级(哲学)
物理
非线性系统
微分方程
精确微分方程
计算机科学
量子力学
一阶偏微分方程
结晶学
人工智能
经济
化学
财务
作者
Zhiheng Yu,Lingling Liu
标识
DOI:10.1142/s0218127420502016
摘要
In this paper, we investigate a quintic Liénard equation which has a center at the origin. We give the conditions for the parameters for the isochronous centers and weak centers of exact order. Then, we present the global phase portraits for the system having isochronous centers. Moreover, we prove that at most four critical periods can bifurcate and show with appropriate perturbations that local bifurcation of critical periods occur from the centers.
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