In this paper by using the Poincaré compactification of ℝ³ we make a global analysis of the model xʹ = ax + y + yz, yʹ = x – ay + bxz, zʹ = cz – bxy. In particular we give the complete description of its dynamics on the infinity sphere. For a + c = 0 or b = 1 this system has invariants. For these values of the parameters we provide the global phase portrait of the system in the Poincaré ball. We also describe the α and ω-limit sets of its orbits in the Poincaré ball.

中文翻译：

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关于三维强迫阻尼微分系统的整体动力学

在本文中使用ℝ的庞加莱紧致³，我们做模型的全局分析Xʹ= ax + y + yz，yʹ= x – ay + bxz，zʹ= cz – bxy。特别是，我们给出了其在无限球体上动力学的完整描述。对于a + c = 0或b = 1，该系统具有不变性。对于这些参数值，我们提供了庞加莱球中系统的全局相图。我们还描述了庞加莱球中轨道的α和ω极限集。