Bifurcation of Periodic Solutions from Steady Ones (Hopf Bifurcation) in Two Dimensions

  • Gérard Iooss
  • Daniel D. Joseph
Part of the Undergraduate Texts in Mathematics book series (UTM)


Up to now the only equilibrium solutions which have been introduced are steady ones. Now we shall show how a time-periodic solution may arise from bifurcation of a steady solution. In this case the symmetry of the forcing data, which is steady, is broken by the time-periodic solution. The dynamical system then has “a mind of its own” in the sense that the solution does not follow the symmetry imposed by the given data.


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Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • Gérard Iooss
    • 1
  • Daniel D. Joseph
    • 2
  1. 1.Faculté des Sciences, Institut des Mathématiques et Sciences PhysiquesUniversité des NiceParc Valrose, NiceFrance
  2. 2.Department of Aerospace Engineering and MechanicsUniversity of MinnesotaMinneapolisUSA

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