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Determining Lyapunov exponents of non-smooth systems: Perturbation vectors approach

机译：确定非光滑系统的Lyapunov指数：摄动向量法

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摘要

This paper presents a novel, simple method of Lyapunov Exponents (LEs) spectrum estimation for non-smooth and discontinuous systems. The presented algorithm works for continuous-time dynamical systems, as well as for discrete maps. Its simplicity and flexibility enables to estimate LEs of complex, discontinuous systems in an easy manner. The paper starts with a comprehensive review of the state-of-art methods of the LEs computation for non-smooth systems. Then, the novel algorithm is introduced. Further on, examples of its use are provided. The presented applications include non-smooth and discontinuous maps, as well as continuous-time mechanical systems with discontinuities induced by impacts or by dry friction. The paper confirms that the method is simple, effective and robust. The presented algorithm can facilitate research in a large class of discontinuous systems, including stick-slip oscillators and many others.
机译：本文提出了一种新颖，简单的非光滑和不连续系统Lyapunov指数（LEs）频谱估计方法。所提出的算法适用于连续时间动力系统以及离散地图。它的简单性和灵活性使您可以轻松估算复杂，不连续系统的LE。本文首先全面回顾了非光滑系统的LE计算的最新方法。然后，介绍了新算法。进一步地，提供了其使用的示例。提出的应用程序包括不平滑和不连续的贴图，以及由于冲击或干摩擦而引起不连续的连续时间机械系统。本文证实了该方法简单，有效，鲁棒。所提出的算法可以促进在大范围的不连续系统中的研究，包括粘滑振荡器和许多其他不连续系统。

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