Testing Critical Slowing Down as a Bifurcation Indicator in a Low-dissipation Dynamical System

TL;DR

This paper examines whether critical slowing down can reliably indicate a bifurcation in a low-dissipation dynamical system, finding that experimental perturbations do not predict bifurcation as theory suggests.

Contribution

The study combines theoretical analysis and experiments to show the limitations of using critical slowing down as a bifurcation indicator in low-dissipation systems.

Findings

Critical slowing down may occur above the bifurcation point.

Experimental perturbations do not alter system behavior to indicate bifurcation.

Theoretical analysis explains why tests fail to predict bifurcations.

Abstract

We study a two-dimensional low-dissipation dynamical system with a control parameter that is swept linearly in time across a transcritical bifurcation. We investigate the relaxation time of a perturbation applied to a variable of the system and we show that critical slowing down may occur at a parameter value well above the bifurcation point. We test experimentally the occurrence of critical slowing down by applying a perturbation to the accessible control parameter and we find that this perturbation leaves the system behavior unaltered, thus providing no useful information on the occurrence of critical slowing down. The theoretical analysis reveals the reasons why these tests fail in predicting an incoming bifurcation.