In this chapter we discuss typical local bifurcations in one and two dimensions. We restrict our attention to bifurcations of codimension 1, which require only one real parameter in order to generically occur. We include several cases of systems that possess an invariance under some simple symmetry.


Normal Form Hopf Bifurcation Phase Portrait Bifurcation Diagram Pitchfork Bifurcation 
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© EDP Sciences 2011

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité de Franche-ComtéBesançon CedexFrance
  2. 2.Laboratoire J.A.DieudonnéIUF, Université de NiceNice Cedex 02France

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