The differential system $\dot x= ax -y z, \ \dot y = -b y + x z, \ \dot z= -c z + x^2,$ where $a$, $b$ and $c$ are positive real parameters, has been studied numerically due to the big variety of strange attractors that it can exhibit. This system has a Darboux invariant when $c=2b$. Using this invariant and the Poincaré compactification technique we describe analytically its global dynamics.
Jaume LIBRE
,
Claudia VALLS
. THE GLOBAL DYNAMICS OF A 3-DIMENSIONAL DIFFERENTIAL SYSTEM IN $\mathbb{R}^3$ VIA A DARBOUX INVARIANT[J]. Acta mathematica scientia, Series B, 2025
, 45(2)
: 338
-346
.
DOI: 10.1007/s10473-025-0204-9
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