Chew L Y, Ting Christopher, Lai C H
School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637616.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Sep;72(3 Pt 2):036222. doi: 10.1103/PhysRevE.72.036222. Epub 2005 Sep 30.
We consider the resonant effects of chaotic fluctuations on a strongly damped particle in a bistable potential driven by weak sinusoidal perturbation. We derive analytical expressions of chaos-induced transition rate between the neighboring potential wells based on the inhomogeneous Smoluchowski equation. Our first-order analysis reveals that the transition rate has the form of the Kramers escape rate except for a perturbed prefactor. This modification to the prefactor is found to arise from the statistical asymmetry of the chaotic noise. By means of the two-state model and the chaos-induced transition rate, we arrive at an analytical expression of the signal-to-noise ratio (SNR). Our first-order SNR shows that chaotic resonance can correspond directly to stochastic resonance.
我们考虑在弱正弦扰动驱动的双稳势中，混沌涨落对强阻尼粒子的共振效应。基于非齐次斯莫卢霍夫斯基方程，我们推导了相邻势阱间混沌诱导跃迁率的解析表达式。我们的一阶分析表明，除了一个受扰的前置因子外，跃迁率具有克拉默斯逃逸率的形式。发现对前置因子的这种修正源于混沌噪声的统计不对称性。借助双态模型和混沌诱导跃迁率，我们得到了信噪比（SNR）的解析表达式。我们的一阶信噪比表明，混沌共振可以直接对应于随机共振。
