In this paper, we use a novel method to investigate the stability of L⬠u u system. It is shown that the L⬠u u system will display a Hopf bifurcation under certain conditions. Finally, we obtain the conditions of supercritical and subcritical bifurcation.
On the Hopf-zero bifurcation of the Michelson system
β Scribed by Jaume Llibre; Xiang Zhang
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 203 KB
- Volume
- 12
- Category
- Article
- ISSN
- 1468-1218
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π SIMILAR VOLUMES
The present work is concerned with the behavior of the second bfurcation of a Hopf bifurcation system excited b,v white-noise. It is found that the intervention of noises induces a dr$t of the bz@rcation point aiong with the subtantial change in bijurcation type.
## Abstract A simple generalization of the Hopf Bifurcation Theorem for scalar higher order ordinary differential equations is suggested. We study the degenerate case where several roots of the characteristic polynomial cross the imaginary axis at the same point for some value __Ξ»__~0~ of the param