One-Parameter Bifurcations of Equilibria in Continuous-Time Systems

  • Yuri A. Kuznetsov
Part of the Applied Mathematical Sciences book series (AMS, volume 112)


In this chapter we formulate conditions defining the simplest bifurcations of equilibria in n-dimensional continuous-time systems: the fold and the Hopf bifurcations. Then we study these bifurcations in the lowest possible dimensions: the fold bifurcation for scalar systems and the Hopf bifurcation for planar systems. Chapter 5 shows how to “lift” these results to n-dimensional situations.


Normal Form Hopf Bifurcation Phase Portrait Nondegeneracy Condition Bibliographical Note 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Yuri A. Kuznetsov
    • 1
    • 2
  1. 1.Centrum voor Wiskunde en InformaticaAmsterdamThe Netherlands
  2. 2.Institute of Mathematical Problems of BiologyRussian Academy of SciencesPushchino, Moscow RegionRussia

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