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.

中文翻译：

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近可积二次多项式系统中四个极限环的可视化

近 40 年来，众所周知，一般平面二次多项式系统可以有四个极限环。最近，在近似可积的二次多项式系统中也发现了四个极限环。为了帮助更多人了解极限环理论，对二次系统中这四个数值模拟极限环的可视化引起了研究者的关注。然而，对于近乎集成的系统，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，我们从 1979 年底左右构建的著名二次系统的模拟开始，然后重新考虑最近发表的具有四个大尺寸极限环的二次系统的模拟，