TY - GEN
T1 - Dynamics of an Electronic Relay Systems with Bandpass Filtered Feedback
AU - Illing, Lucas
AU - Benkendorfer, Kees
AU - Ryan, Pierce
AU - Amann, Andreas
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - Delay dynamics have wide relevance in fundamental science and technology due to the ubiquitous presence of feedback loops in which time lags arise because of natural processes, control interfaces, or performance limits of components. We present results from a well-controlled experiment that is representative of feedback systems with relays (switches) that actuate after a fixed delay. Notably, the system exhibits strong multirhythmicity, the coexistence of many stable periodic solutions for the same values of parameters. We then study the system dynamics analytically. The model we consider is a nonsmooth second-order delay differential equation that describes single-input single-output systems in which the delayed feedback is a bandpass filtered relay signal. We discuss how periodic solutions and bifurcations can be obtained by reducing the system to a set of finite-dimensional maps. We find good agreement between theory and experiment.
AB - Delay dynamics have wide relevance in fundamental science and technology due to the ubiquitous presence of feedback loops in which time lags arise because of natural processes, control interfaces, or performance limits of components. We present results from a well-controlled experiment that is representative of feedback systems with relays (switches) that actuate after a fixed delay. Notably, the system exhibits strong multirhythmicity, the coexistence of many stable periodic solutions for the same values of parameters. We then study the system dynamics analytically. The model we consider is a nonsmooth second-order delay differential equation that describes single-input single-output systems in which the delayed feedback is a bandpass filtered relay signal. We discuss how periodic solutions and bifurcations can be obtained by reducing the system to a set of finite-dimensional maps. We find good agreement between theory and experiment.
KW - Bifurcations
KW - Delay differential equations
KW - Nonlinear circuits
KW - Nonlinear dynamics
KW - Nonsmooth dynamical systems
KW - Quasiperiodic oscillations
KW - Relay systems
UR - https://www.scopus.com/pages/publications/85218045000
U2 - 10.1007/978-3-031-60907-7_17
DO - 10.1007/978-3-031-60907-7_17
M3 - Conference proceeding
AN - SCOPUS:85218045000
SN - 9783031609060
T3 - Springer Proceedings in Complexity
SP - 217
EP - 230
BT - 16th Chaotic Modeling and Simulation International Conference
A2 - Skiadas, Christos H.
A2 - Dimotikalis, Yiannis
PB - Springer Science and Business Media B.V.
T2 - 16th Chaotic Modeling and Simulation International Conference, CHAOS 2023
Y2 - 13 June 2023 through 17 June 2023
ER -