Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria

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


In this chapter we will study global bifurcations corresponding to the appearance of homoclinic or heteroclinic orbits connecting hyperbolic equilibria in continuous-time dynamical systems. We will consider in detail two- and three-dimensional cases for two reasons: first, because in these cases geometrical intuition can be fully exploited, and second, because all the main results can be generalized to higher dimensions.


Phase Portrait Invariant Manifold Unstable Manifold Homoclinic Orbit Heteroclinic Orbit 
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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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