Transient chaos in time-delayed systems subjected to parameter drift
Abstract
External and internal factors may cause a system's parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a time-delayed oscillator whose time delay varies at a small but non-negligible rate. Our research shows that due to this parameter drift, trajectories from a chaotic attractor tip to other states with a certain probability. This causes the appearance of the phenomenon of transient chaos. By using an ensemble approach, we find a gamma distribution of transient lifetimes, unlike in other non-delayed systems where normal distributions have been found to govern the process. Furthermore, we analyze how the parameter change rate influences the tipping probability, and we derive a scaling law relating the parameter value for which the tipping takes place and the lifetime of the transient chaos with the parameter change rate.
Cite
@article{arxiv.2010.06244,
title = {Transient chaos in time-delayed systems subjected to parameter drift},
author = {Julia Cantisán and Jesús M. Seoane and Miguel A. F. Sanjuán},
journal= {arXiv preprint arXiv:2010.06244},
year = {2020}
}