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Degenerate Poincaré-Andronov-Hopf Bifurcation

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

Abstract

In this chapter we study the Poincaré-Andronov-Hopf bifurcation without parameters, see Chap. 5, with an additional degeneracy of the drift or transversality due to an additional parameter or an additional dimension of the primary manifold of equilibria.

Keywords

  • Periodic Orbit
  • Normal Form
  • Imaginary Eigenvalue
  • Extended Phase Space
  • Equilibrium Plane

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Fig. 9.1
Fig. 9.2
Fig. 9.3
Fig. 9.4

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). Degenerate Poincaré-Andronov-Hopf Bifurcation. In: Bifurcation without Parameters. Lecture Notes in Mathematics, vol 2117. Springer, Cham. https://doi.org/10.1007/978-3-319-10777-6_9

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