Key Laboratory in Universities for Radiation Beam Technology and Materials Modification,Institute of Low Energy Nuclear Physics, Beijing Normal University, Beijing 100875
Hopf Bifurcation in a Nonlinear Wave System
HE Kai-Fen
Key Laboratory in Universities for Radiation Beam Technology and Materials Modification,Institute of Low Energy Nuclear Physics, Beijing Normal University, Beijing 100875
Abstract： Bifurcation behaviour of a nonlinear wave system is studied by utilizing the data in solving the nonlinear wave equation. By shifting to the steady wave frame and taking into account the Doppler effect, the nonlinear wave can be transformed into a set of coupled oscillators with its (stable or unstable) steady wave as the fixed point. It is found that in the chosen parameter regime, both mode amplitudes and phases of the wave can bifurcate to limit cycles attributed to the Hopf instability. It is emphasized that the investigation is carried out in a pure nonlinear wave framework, and the method can be used for further exploration of the routes to turbulence.
(Waves, oscillations, and instabilities in plasmas and intense beams)
引用本文:
HE Kai-Fen. Hopf Bifurcation in a Nonlinear Wave System[J]. 中国物理快报, 2004, 21(3): 439-442.
HE Kai-Fen. Hopf Bifurcation in a Nonlinear Wave System. Chin. Phys. Lett., 2004, 21(3): 439-442.
2004, Vol. 21 
