Numerical approximation and spectral analysis of infinite-dimensional dynamical systems
03-048 Yong-Kui Zou, Tassilo Küpper, Wolf-Jürgen Beyn.
Generalized Hopf bifurcation for non-smooth planar
dynamical systems
In this paper, we study the existence
of periodic orbits bifurcating from stationary solutions in a
non-smooth planar dynamical system. This phenomenon is
interpreted as generalized Hopf bifurcation. In the case of
smoothness, Hopf bifurcation is characterized by a pair of
complex conjugate eigenvalues crossing through the pure
imaginary axis. This method does not apply to a non-smooth
system due to the lack of linearization. In fact, the
generalized Hopf bifurcation is determined by interactions
between the discontinuity of the system and the eigenstructure
of each subsystem. We combine a geometrical method and an
analytical method to investigate the generalized Hopf
bifurcation. The bifurcating periodic orbits are obtained by
studying the fixed points of return maps.
