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)’.

中文翻译：

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用确定性激励来表示噪声以解释随机共振现象

向系统添加噪声可以“改善”其动态行为，例如，它可以增加其响应或信噪比。相应的现象称为随机共振，已在物理学、神经科学、生物学、医学和力学中得到了大量应用。用高频激励代替随机激励被证明是分析几种线性和非线性动态系统的可行方法。对于这些系统，随机激励和高频激励的影响在性质上是相似的。本文讨论了这种“确定性”方法对随机系统的适用性。首先，简要回顾一下传统的非线性双稳态系统。然后考虑具有乘性噪声的动力系统，并讨论了用确定性激励代替此类系统的随机激励的有效性。最后，我们研究具有非线性阻尼的振荡系统，并分析随机和确定性激励对此类系统的影响。本文是主题问题“驱动非线性系统中的振动和随机共振（第 1 部分）”的一部分。