On the Hopf-zero bifurcation of the Michelson system

Jaume Llibre, Xiang Zhang

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23 Citations (Scopus)


Applying a new result for studying the periodic orbits of a differential system via the averaging theory, we provide the first analytic proof of the existence of a Hopf-zero bifurcation for the Michelson system x=y,y=z,z= c2-y-x22, at c=0. Moreover our method estimates the shape of this periodic orbit as a function of c>0, sufficiently small. © 2010 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)1650-1653
JournalNonlinear Analysis: Real World Applications
Publication statusPublished - 1 Jun 2011


  • Averaging method
  • Hopf bifurcation
  • Michelson system
  • Periodic orbit


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