噪声诱导Hopf分岔
Noise induced Hopf bifurcation
摘要：
我们考虑了随机源对系统自组织过程的影响，系统自组织过程是由Hopf分岔引起的极限环的产生而开始的。将所得的一般关系应用于随机Lorenz系统，表明偏离平衡定态可以破坏极限环，这依赖于主变量随时间变化的特征尺度之间的关系。如果最快的变化显示一个主变量，这是耦合到两个不同的自由度或更多的噪声引起的共振有关的极限环。
英文摘要：
We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle induced by the Hopf bifurcation. General relations obtained are applied to the stochastic Lorenz system to show that departure from equilibrium steady state can destroy the limit cycle in dependence of relation between characteristic scales of temporal variation of principle variables. Noise induced resonance related to the limit cycle is found to appear if the fastest variations displays a principle variable, which is coupled with two different degrees of freedom or more.
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