Nonlinear systems are abundant in nature. Their dynamics have been investigated very extensively, motivated partly by their multidisciplinary applicability, ranging from all branches of physical and mathematical sciences through engineering to the life sciences and medicine. When driven by external forces, nonlinear systems can exhibit a plethora of interesting and important properties—one of the most prominent being that of resonance. In the presence of a second, higher frequency, driving force, whether stochastic or deterministic/periodic, a resonance phenomenon arises that can generally be termed stochastic resonance or vibrational resonance. Operating a system in or out of resonance promises applications in several advanced technologies, such as the creation of novel materials at the nano, micro and macroscales including, but not limited to, materials having photonic band gaps, quantum control of atoms and molecules as well as miniature condensed matter systems. Motivated in part by these potential applications, this 2-part Theme Issue provides a concrete up-to-date overview of vibrational and stochastic resonances in driven nonlinear systems. It assembles state-of-the-art, original contributions on such induced resonances—addressing their analysis, occurrence and applications from either the theoretical, numerical or experimental perspectives, or through combinations of these. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

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驱动非线性系统中的振动和随机共振

非线性系统在自然界中非常丰富。它们的动力学已经被非常广泛地研究，部分原因是它们的多学科适用性，从物理和数学科学的所有分支到工程学，再到生命科学和医学。当受外力驱动时，非线性系统会表现出大量有趣且重要的特性——其中最突出的特性之一是共振特性。在存在第二个更高频率的驱动力时，无论是随机的还是确定性的/周期性的，都会出现共振现象，通常可以称为随机共振或振动共振。在共振内或共振外运行系统有望应用于多种先进技术，例如在纳米、微米和宏观尺度上创造新材料，包括但不限于，具有光子带隙、原子和分子的量子控制以及微型凝聚态系统的材料。部分受这些潜在应用的启发，这个由 2 部分组成的主题问题提供了驱动非线性系统中振动和随机共振的具体最新概述。它汇集了对此类感应共振的最先进的原创贡献——从理论、数值或实验的角度或通过这些的组合来解决它们的分析、发生和应用。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。这个由两部分组成的主题问题提供了驱动非线性系统中振动和随机共振的具体最新概述。它汇集了对此类感应共振的最先进的原创贡献——从理论、数值或实验的角度或通过这些的组合来解决它们的分析、发生和应用。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。这个由两部分组成的主题问题提供了驱动非线性系统中振动和随机共振的具体最新概述。它汇集了对此类感应共振的最先进的原创贡献——从理论、数值或实验的角度或通过这些的组合来解决它们的分析、发生和应用。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。