THE GLOBAL DYNAMICS OF A 3-DIMENSIONAL DIFFERENTIAL SYSTEM IN R^(3) VIA A DARBOUX INVARIANT  

作　　者：Jaume LLIBRE Claudia VALLS 

机构地区：[1]Departament de Matematiques,Universitat Autònoma de Barcelona,08193,Bellaterra,Barcelona,Catalonia,Spain [2]Departamento de Matemática,Instituto Superior Técnico,Universidade de Lisboa,Av.Rovisco Pais,1049-001,Lisboa,Portugal

出　　处：《Acta Mathematica Scientia》2025年第2期338-346,共9页数学物理学报(B辑英文版)

基　　金：supported by the Agencia Estatal de Investigación grant PID2019-104658GB-I00;the H2020 European Research Council grant MSCA-RISE-2017-777911;AGAUR(Generalitat de Catalunya)grant 2021SGR00113;the Reial Acadèmia de Ciències i Arts de Barcelona;supported by FCT/Portugal through CAMGSD,IST-ID,projects UIDB/04459/2020 and UIDP/04459/2020.

摘　　要：The differential systemẋ=ax−yz,ẏ=−by+xz,ż=−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 Poincarécompactification technique we describe analytically its global dynamics.

关 键 词：INVARIANT Poincare ball Poincarédisc w-limit Q-limit differential system in R^(3) 

分 类 号：O175[理学—数学]