A Note on the Triple-Zero Linear Degeneracy: Normal Forms, Dynamical and bifurcation Behaviors of an Unfolding
نویسندگان
چکیده
This paper is devoted to the analysis of bifurcations in a three-parameter unfolding of a linear degeneracy corresponding to a triple-zero eigenvalue. We carry out the study of codimensiontwo local bifurcations of equilibria (Takens–Bogdanov and Hopf-zero) and show that they are nondegenerate. This allows to put in evidence the presence of several kinds of bifurcations of periodic orbits (secondary Hopf, . . .) and of global phenomena (homoclinic, heteroclinic). The results obtained are applied in the study of the Rössler equation.
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ورودعنوان ژورنال:
- I. J. Bifurcation and Chaos
دوره 12 شماره
صفحات -
تاریخ انتشار 2002