@article{6439bf5c27ce4bcba5d2a82c32a9ea7d,
title = "The Global Dynamics of a 3-Dimensional Differential System in ℝ3 via a Darboux Invariant",
abstract = "The differential system ẋ = ax − yz, ẏ = −by + xz, {\.z} = −cz + x2, 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 Poincar{\'e} compactification technique we describe analytically its global dynamics.",
keywords = "34C25, 34C29, 47H11, Poincar{\'e} ball, Poincar{\'e} disc, differential system in ℝ, invariant, α-limit, ω-limit, Invariant, Poincare ball, differential system in R-3, Alpha-limit, Poincare disc, Omega-limit",
author = "Jaume Llibre and Cl{\`a}udia Valls",
note = "Publisher Copyright: {\textcopyright} Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences 2025.",
year = "2024",
month = nov,
day = "16",
doi = "10.1007/s10473-025-0204-9",
language = "English",
volume = "45",
pages = "338--346",
journal = "Acta Mathematica Scientia",
issn = "0252-9602",
publisher = "Elsevier",
number = "2",
}