Abstract
In this article we study the Darboux integrability of the polynomial differential systems \[ \dot x = y-x^2, \quad \dot y=z-x, \quad \dot z= -d-ax -by-cz. \] This system comes from the study of a Hopf bifurcation in slow-fast systems with two slow variables and one fast variable. The tools used here for studying the Darboux integrability can be applied to arbitrary polynomial differential systems in $\mathbb R^3$.
Citation
Jaume Llibre. Clàudia Valls. "Darboux integrability of polynomial differential systems in $\mathbb R^3$." Bull. Belg. Math. Soc. Simon Stevin 20 (4) 603 - 619, october 2013. https://doi.org/10.36045/bbms/1382448183
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