On the global dynamics of the Rabinovich system

Jaume Llibre, Marcelo Messias, Paulo R. Da Silva

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47 Citations (Scopus)


In this paper by using the Poincaré compactification in we make a global analysis of the Rabinovich system with and . We give the complete description of its dynamics on the sphere at infinity. For ten sets of the parameter values the system has either first integrals or invariants. For these ten sets we provide the global phase portrait of the Rabinovich system in the Poincaré ball (i.e. in the compactification of with the sphere of the infinity). We prove that for convenient values of the parameters the system has two families of singularly degenerate heteroclinic cycles. Then changing slightly the parameters we numerically found a four wings butterfly shaped strange attractor. © 2008 IOP Publishing Ltd.
Original languageEnglish
Article number275210
JournalJournal of Physics A: Mathematical and Theoretical
Publication statusPublished - 11 Jul 2008


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