Two-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems

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


This chapter is devoted to the study of generic bifurcations of fixed points of two-parameter maps. First we derive a list of such bifurcations. As for the final two bifurcations in the previous chapter, the description of the majority of these bifurcations is incomplete in principle. For all but two cases, only approximate normal forms can be constructed. Some of these normal forms will be presented in terms of associated planar continuous-time systems whose evolution operator φ 1 approximates the map in question (or an appropriate number of iterates of the map). We present bifurcation diagrams of the approximate normal forms and discuss their relationships with the original maps.


Hopf Bifurcation Bifurcation Diagram Center Manifold Bifurcation Curve Heteroclinic Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations