Related Experiment Video
Updated: Dec 6, 2025

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Testing Critical Slowing Down as a Bifurcation Indicator in a Low-Dissipation Dynamical System
M Marconi1, C Métayer2, A Acquaviva1
1Université Côte d' Azur, Institut de Physique de Nice, CNRS-UMR 7010, Sophia Antipolis, France.
Abstract:
We study a two-dimensional low-dissipation nonautonomous 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.
More Related Videos
Related Concept Videos
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
Types of Damping
Transmission-Line Differential Equations
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...
Limits with Oscillating Discontinuities
Second Order systems II
Transient and Steady-state Response
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state...

