Testing Critical Slowing Down as a Bifurcation Indicator in a Low-dissipation Dynamical System
Pattern Formation and Solitons
2020-09-30 v1 Chaotic Dynamics
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.
Cite
@article{arxiv.2008.10451,
title = {Testing Critical Slowing Down as a Bifurcation Indicator in a Low-dissipation Dynamical System},
author = {M. Marconi and C. Metayer and A. Acquaviva and J. M. Boyer and A. Gomel and T. Quiniou and C. Masoller and M. Giudici and J. R. Tredicce},
journal= {arXiv preprint arXiv:2008.10451},
year = {2020}
}