Dynamics of a time-delayed relay system

Illing, Lucas; Ryan, Pierce; Amann, Andreas

Dynamics of a time-delayed relay system

Files

PhysRevE.109.014223.pdf(1.42 MB)

Published Version

Date

2024-01-23

Authors

Illing, Lucas

Ryan, Pierce

Amann, Andreas

Publisher

American Physical Society

Published Version

https://doi.org/10.1103/PhysRevE.109.014223

Abstract

We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong multirhythmicity, the coexistence of many stable periodic solutions for the same values of the parameters. We present a detailed study of these periodic solutions and their bifurcations. Starting from an integrodifferential model, we show how to reduce the system to a set of finite-dimensional maps. We then demonstrate that the parameter regions of existence of periodic solutions can be understood in terms of discontinuity-induced bifurcations and their stability is determined by smooth bifurcations. Using this technique, we are able to show that slowly oscillating solutions are always stable if they exist. We also demonstrate the coexistence of stable periodic solutions with quasiperiodic solutions.

Keywords

Time-delayed relay system , Feedback systems with relays , Multirhythmicity

Citation

Illing, L., Ryan, P. and Amann, A. (2024) 'Dynamics of a time-delayed relay system', Physical Review E, 109(1), 014223 (12pp). doi: https://doi.org/10.1103/PhysRevE.109.014223