The first objective of this paper is to study the Darboux integrability of the polynomial differential system$\dot{x}=y,\dot{y}=-x-yz,\dot{z}=y^2-a$ and the second one is to show that for $a>0$ sufficiently small this model exhibits one small amplitude periodic solution that bifurcates from the origin of coordinates when $a=0$. This model was introduced by Hoover as the first example of a differential equation with a hidden attractor and it was used by Sprott to illustrate a differential equation having a chaotic behavior without equilibrium points, and now this system is known as the Sprott A system.

中文翻译：

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Sprott A系统中的可积性和零霍夫分支

本文的首要目标是研究多项式微分系统的Darboux可积性$\dot{X}=ÿ，\dot{ÿ}=-X-ÿž，\dot{ž}={ÿ}^2-\mathrm{一种}$ 第二个是为了证明 $\mathrm{一种}>0$ 足够小，该模型表现出一个小幅度的周期解，该周期解从坐标原点分叉 $\mathrm{一种}=0$。该模型是由Hoover引入的，它是带有隐藏吸引子的微分方程的第一个示例，并且由Sprott用来说明具有无平衡点的混沌行为的微分方程，现在该系统被称为Sprott A系统。