标题： 非线性动力学中的实验延拓：近期进展与未来挑战 显示英文标题

标题： Experimental continuation in nonlinear dynamics: recent advances and future challenges

摘要： 实验延拓法是一组结合控制与延拓的方法，能够在实验中获取非线性系统的完整分岔图，包括在无反馈控制情况下系统中会不稳定的响应。 因此，基于这种控制的方法使实验者能够直接且全面地探索系统的动力学特性，而无需良好的数学模型。 本文的目的有两个，一是以统一的方式回顾并呈现最先进的方法；二是介绍一种新颖的基于控制的无导数弧长延拓程序，称为基于弧长控制的延拓。 这些方法还在一个电子杜芬振子和一个具有几何非线性的夹紧薄板上进行了演示和比较。 最后，反思了当前的研究状态，并讨论了该领域面临的挑战。 显示英文摘要

摘要： Experimental continuation encompasses a set of methods that combine control and continuation to obtain the full bifurcation diagram of a nonlinear system experimentally, including responses that would be unstable in the system without feedback control. Such control-based methods thus allow the experimenter to directly and exhaustively explore the dynamics of the system without the need for a good mathematical model. The objective of this paper is twofold, namely (i) to review and present the state-of-the-art methods in a unified manner and (ii) to introduce a novel experimental derivative-free arclength continuation procedure, termed arclength control-based continuation. These methods are also demonstrated and compared on an electronic Duffing oscillator and a clamped thin plate featuring geometrical nonlinearity. Finally, the current state of the art is reflected upon, and the challenges lying ahead for this growing field are discussed.