Experimental continuation in nonlinear dynamics: recent advances and future challenges

TL;DR

This paper reviews recent experimental continuation methods for nonlinear systems, introduces a new derivative-free arclength continuation technique, and demonstrates its application on electronic and mechanical nonlinear systems, highlighting future challenges.

Contribution

It presents a unified review of experimental continuation methods and introduces a novel derivative-free arclength continuation approach for nonlinear dynamics.

Findings

The new method successfully applied to electronic Duffing oscillator.

Demonstrated on a nonlinear thin plate with geometrical nonlinearity.

Compared with existing methods, showing advantages in certain scenarios.

Abstract

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.