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One-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems

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

Abstract

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. Appendixes A and B are devoted to technical questions appearing in the analysis of Hopf bifurcation: Effects of higher-order terms and a general theory of Poincaré normal forms, respectively. Chapter 5 shows how to “lift” the results of this chapter to n-dimensional situations.

Keywords

Normal Form Hopf Bifurcation Fold Bifurcation Normal Form Theory Resonant Term 
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.

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Bibliographical notes

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Yuri A. Kuznetsov
    • 1
    • 2
  1. 1.Department of MathematicsUtrecht UniversityUtrechtThe Netherlands
  2. 2.Institute of Mathematical Problems of BiologyRussian Academy of SciencesPushchino, Moscow RegionRussia

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