%0 Journal Article
%T ON THE HOPF BIFURCATION SYSTEM IN THE PRESENCE OF PARAMETRIC REAL NOISES<br>实噪声参激Hopf分叉系统研究
%A Liu Xianbin
%A Chen Qiu Dept of Engrg Mech
%A Southwest Jiaotong University
%A Chengdu
%A China
%A <br>刘先斌
%A 陈虬
%J 力学学报
%D 1997
%I 
%X With the aid of the stochastic averaging method,the theory of singular points of diffusion processes and the method of invariant measure, a Hopf bifurcation system in the presence of parametric real noises is studied. It is found that in this nonlinear stochastic system, due tothe presence of the parametric real noises, a change of the type of bifurcation takes place and two bifurcation points appear, which differ from the original Hopf bifurcation one.
%K real noise
%K parametric excitation
%K stochastic averaging method
%K diffusion process
%K singular boundary
%K invariant measure
%K stochastic bifurcation<br>实噪声
%K 参数激励
%K 噪声
%K 随机分叉
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=5D344E2AD54D14F8&jid=4100DA4A1A3BA1B0CE5AD99AE1DFB420&aid=AE6D6FBC5E5081AC05596A79AA29EC7A&yid=5370399DC954B911&vid=771469D9D58C34FF&iid=0B39A22176CE99FB&sid=4C100B7696CE9E24&eid=43608FD2E15CD61B&journal_id=0459-1879&journal_name=力学学报&referenced_num=3&reference_num=4