Abstract
The final bifurcation of codimension 2 is characterized by the intersection of 2 curves of Poincaré-Andronov-Hopf points on a two-dimensional surface of equilibria. As we shall see, the drift direction at the Hopf lines play an important role. In the case of a parameter-dependent fixed line of equilibria, drifts at both Hopf-lines can be opposite and spiraling orbits appear, see Sect. 12.1. In the generic case with a plane of equilibria without parameters, both drifts are transverse and generate a Lyapunov function. Only heteroclinic orbits arise. See Sect. 12.2.
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References
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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Liebscher, S. (2015). Double-Hopf Bifurcation. In: Bifurcation without Parameters. Lecture Notes in Mathematics, vol 2117. Springer, Cham. https://doi.org/10.1007/978-3-319-10777-6_12
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DOI: https://doi.org/10.1007/978-3-319-10777-6_12
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