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Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria

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Elements of Applied Bifurcation Theory

Part of the book series: Applied Mathematical Sciences ((AMS,volume 112))

Abstract

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. First we consider in detail two- and three-dimensional cases where geometrical intuition can be fully exploited. Then we show how to reduce generic n-dimensional cases to the considered ones plus a four-dimensional case treated in Appendix A.

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Authors and Affiliations

  1. Department of Mathematics, Utrecht University, Budapestlaan 6, 3584 CD, Utrecht, The Netherlands

    Yuri A. Kuznetsov

  2. Institute of Mathematical Problems of Biology, Russian Academy of Sciences, 142290, Pushchino, Moscow Region, Russia

    Yuri A. Kuznetsov

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  1. Yuri A. Kuznetsov
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Kuznetsov, Y.A. (2004). Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria. In: Elements of Applied Bifurcation Theory. Applied Mathematical Sciences, vol 112. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3978-7_6

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  • DOI: https://doi.org/10.1007/978-1-4757-3978-7_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-1951-9

  • Online ISBN: 978-1-4757-3978-7

  • eBook Packages: Springer Book Archive

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