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Zero-Hopf Bifurcation

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2117)

Abstract

In this chapter we study a bifurcation characterized by a zero eigenvalue and a pair of nonzero purely imaginary eigenvalues of the linearization transverse to a plane of equilibria. It turns out that instead we can study a one-parameter family of lines in a system depending on one parameter. Indeed, the rescaled normal form (11.6) is the same in both cases.

Keywords

  • Normal Form
  • Center Manifold
  • Zero Eigenvalue
  • Heteroclinic Orbit
  • Singular Boundary

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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Fig. 11.1

References

  1. Vanderbauwhede, A.: Centre manifolds, normal forms and elementary bifurcations. In: Kirchgraber, U., Walther, H.O. (eds.) Dynamics Reported 2, pp. 89–169. Teubner & Wiley, Stuttgart (1989)

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© 2015 Springer International Publishing Switzerland

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Liebscher, S. (2015). Zero-Hopf Bifurcation. In: Bifurcation without Parameters. Lecture Notes in Mathematics, vol 2117. Springer, Cham. https://doi.org/10.1007/978-3-319-10777-6_11

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