Dresden 2026 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 48: Nonlinear Dynamics and Time-Delay Systems
DY 48.5: Talk
Thursday, March 12, 2026, 10:30–10:45, ZEU/0118
FPGA-integrated analog simulations of time-delayed differential equations — •Matthias Hering1, Julien Javaloyes2, and Svetlana V. Gurevich1,2,3 — 1Institute of Theoretical Physics, Münster, Germany — 2Departament de Física and IAC3, Universitat de les Illes Balears, Spain — 3Center for Data Science and Complexity, Münster, Germany
Real-world complex systems can be strongly influenced by time-delays due to unavoidable finite signal propagation speeds and time-delayed dynamical systems (TDSs) have proven to be a fertile framework for the modeling of nonlinear phenomena. However, they are difficult to study experimentally due to the need for precise delay elements. We present a hybrid implementation by integrating a digital feedback loop powered by an FPGA into an analog circuit to realize a damped harmonic oscillator with a piecewise nonlinear, delayed restoring force. Operating at 125 MS/s enables the FPGA to enable a clean reconstruction of the system*s dynamics up into the MHz regime without digital artifacts. The experiment not only reproduces the expected Turing bifurcation in the long delay limit, but also reveals the formation of robust localized states and square-waves patterns.
Keywords: field-programmable gate array; time-delayed feedback; long delay limit; localized states; piecewise nonlinearity