Department of Mechanical Engineering, University of Auckland, Bldg 405 Level 8, Room 851, Auckland 1010, New Zealand.
Mehanobr-Tekhnika Research and Engineering Corp. 3, 22 Liniya, V.O., St. Petersburg, Russia 199106.
Philos Trans A Math Phys Eng Sci. 2021 Mar 8;379(2192):20200229. doi: 10.1098/rsta.2020.0229. Epub 2021 Jan 18.
Adding noise to a system can 'improve' its dynamic behaviour, for example, it can increase its response or signal-to-noise ratio. The corresponding phenomenon, called stochastic resonance, has found numerous applications in physics, neuroscience, biology, medicine and mechanics. Replacing stochastic excitations with high-frequency ones was shown to be a viable approach to analysing several linear and nonlinear dynamic systems. For these systems, the influence of the stochastic and high-frequency excitations appears to be qualitatively similar. The present paper concerns the discussion of the applicability of this 'deterministic' approach to stochastic systems. First, the conventional nonlinear bi-stable system is briefly revisited. Then dynamical systems with multiplicative noise are considered and the validity of replacing stochastic excitations with deterministic ones for such systems is discussed. Finally, we study oscillatory systems with nonlinear damping and analyse the effects of stochastic and deterministic excitations on such systems. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.
向系统中添加噪声可以“改善”其动态行为，例如，增加其响应或信噪比。这种被称为随机共振的现象在物理学、神经科学、生物学、医学和力学中得到了广泛的应用。用高频随机激励代替随机激励已被证明是分析几种线性和非线性动力系统的可行方法。对于这些系统，随机和高频激励的影响似乎在性质上是相似的。本文讨论了这种“确定性”方法在随机系统中的适用性。首先，简要回顾了传统的非线性双稳态系统。然后考虑了具有乘性噪声的动力系统，并讨论了用确定性激励代替随机激励的有效性。最后，我们研究了具有非线性阻尼的振荡系统，并分析了随机和确定性激励对这类系统的影响。本文是主题为“受激非线性系统中的振动和随机共振（第 1 部分）”的一部分。
