This study focuses on characterising numerically the attractor volume in the state space of dynamical systems excited by additive white noise. A definition for stochastic attractors is introduced in terms of probability measure and numerical methodologies are presented to characterise them. The study is limited to investigating the effects of additive noise on fixed point and limit cycle attractors of the corresponding noise free system. The effect of noise intensity on the definition and validity of the proposed methodology is also discussed.

中文翻译：

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表征具有加性噪声的动力系统的随机不动点和极限环

这项研究着重于数值表征由加性白噪声激发的动力系统的状态空间中的吸引子体积。根据概率测度引入了随机吸引子的定义，并提出了数值方法对其进行表征。该研究仅限于研究附加噪声对相应无噪声系统的固定点和极限循环吸引子的影响。还讨论了噪声强度对所提出方法的定义和有效性的影响。