Abstract
The first objective of this paper is to study the Darboux integrability of the polynomial differential systemx˙=y,y˙=−x−yz,z˙=y2−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.
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