The Hopf bifurcation in the Shimizu–Morioka system

Jaume Llibre, Claudio Pessoa

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11 Citations (Scopus)


© 2014, Springer Science+Business Media Dordrecht. We study the local Hopf bifurcations of codimension one and two, which occur in the Shimizu–Morioka system. This system is a simplified model proposed for studying the dynamics of the well-known Lorenz system for large Rayleigh numbers. We present an analytic study and their bifurcation diagrams of these kinds of Hopf bifurcation, showing the qualitative changes in the dynamics of its solutions for different values of the parameters.
Original languageEnglish
Pages (from-to)2197-2205
JournalNonlinear Dynamics
Issue number3
Publication statusPublished - 1 Jan 2014


  • Bifurcation diagram
  • Hopf bifurcation
  • Limit cycles


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