Generalized Hopf bifurcation for planar Filippov systems continuous at the origin

Zou Y, Küpper T, Beyn W-J (2006)
Journal of Nonlinear Science 16(2): 159-177.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Zou, Yongkui; Küpper, Tassilo; Beyn, Wolf-JürgenUniBi
Abstract / Bemerkung
In this paper, we study the existence of periodic orbits bifurcating from stationary solutions of a planar dynamical system of Filippov type. This phenomenon is interpreted as a generalized Hopf bifurcation. In the case of smoothness, Hopf bifurcation is characterized by a pair of complex conjugate eigenvalues crossing through the imaginary axis. This method does not carry over to nonsmooth systems, due to the lack of linearization at the origin which is located on the line of discontinuity. In fact, generalized Hopf bifurcation is determined by interactions between the discontinuity of the system and the eigen-structures of all subsystems. With the help of geometrical observations for a corresponding piecewise linear system, we derive an analytical method to investigate the existence of periodic orbits that are obtained by searching for the fixed points of return maps.
Stichworte
Hopf bifurcation; Filippov system; return map
Erscheinungsjahr
2006
Zeitschriftentitel
Journal of Nonlinear Science
Band
16
Ausgabe
2
Seite(n)
159-177
ISSN
0938-8974
Page URI
https://pub.uni-bielefeld.de/record/1599628

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Zou Y, Küpper T, Beyn W-J. Generalized Hopf bifurcation for planar Filippov systems continuous at the origin. Journal of Nonlinear Science. 2006;16(2):159-177.
Zou, Y., Küpper, T., & Beyn, W. - J. (2006). Generalized Hopf bifurcation for planar Filippov systems continuous at the origin. Journal of Nonlinear Science, 16(2), 159-177. https://doi.org/10.1007/s00332-005-0606-8
Zou, Y., Küpper, T., and Beyn, W. - J. (2006). Generalized Hopf bifurcation for planar Filippov systems continuous at the origin. Journal of Nonlinear Science 16, 159-177.
Zou, Y., Küpper, T., & Beyn, W.-J., 2006. Generalized Hopf bifurcation for planar Filippov systems continuous at the origin. Journal of Nonlinear Science, 16(2), p 159-177.
Y. Zou, T. Küpper, and W.-J. Beyn, “Generalized Hopf bifurcation for planar Filippov systems continuous at the origin”, Journal of Nonlinear Science, vol. 16, 2006, pp. 159-177.
Zou, Y., Küpper, T., Beyn, W.-J.: Generalized Hopf bifurcation for planar Filippov systems continuous at the origin. Journal of Nonlinear Science. 16, 159-177 (2006).
Zou, Yongkui, Küpper, Tassilo, and Beyn, Wolf-Jürgen. “Generalized Hopf bifurcation for planar Filippov systems continuous at the origin”. Journal of Nonlinear Science 16.2 (2006): 159-177.

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