论文标题
在近乎综合的二级多项式系统中的四个极限周期的可视化
Visualization of Four Limit Cycles in Near-Integrable Quadratic Polynomial Systems
论文作者
论文摘要
近40美元的闻名，普通平面二次多项式系统可以具有四个极限周期。最近，在近乎综合的四级多项式系统中也发现了四个极限周期。为了帮助更多的人理解限制周期理论，在二次系统中，这种数值模拟的极限周期的可视化吸引了研究人员的注意。但是，对于接近积分的系统，由于选择参数值的限制，这种可视化变得更加困难。在本文中，我们始于1979年底左右构建的著名二次系统的模拟，然后重新考虑了最近发表的二次系统的模拟，该系统展示了四个大尺寸限制周期，最后提供了一个混凝土近乎构成的综合Quadratic多项式系统，以显示出四个正常尺寸的极限周期。
It has been known for almost $40$ years that general planar quadratic polynomial systems can have four limit cycles. Recently, four limit cycles were also found in near-integrable quadratic polynomial systems. To help more people to understand limit cycles theory, the visualization of such four numerically simulated limit cycles in quadratic systems has attracted researchers' attention. However, for near integral systems, such visualization becomes much more difficult due to limitation on choosing parameter values. In this paper, we start from the simulation of the well-known quadratic systems constructed around the end of 1979, then reconsider the simulation of a recently published quadratic system which exhibits four big size limit cycles, and finally provide a concrete near-integral quadratic polynomial system to show four normal size limit cycles.
