实噪声参激Hopf分叉系统研究
ON THE HOPF BIFURCATION SYSTEM IN THE PRESENCE OF PARAMETRIC REAL NOISES
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摘要: 采用随机平均法、扩散过程的奇点理论、不变测度方法分析了实噪声参激的分叉系统.明确了噪声的影响将使系统出现与原分叉点不同的噪声导致的分叉点,并使分叉类型产生了根本的改变Abstract: 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.