About Me

My research focuses on dynamical systems theory and its applications to nonlinear optics and mathematical biology among others. I specialize in analytical and numerical methods for delay differential and functional differential equations when the delay is large compared to other time scales of the system. Some of my specific contributions involve the fixed point spectrum for large delay, as well as the characterization of slowly oscillating solutions, such as traveling pulses and waves. My future research is dedicated to applying these techniques to delay and lattice dynamical systems arising from coupled excitable and coupled bi-stable systems in laser dynamics and neuroscience, where these solutions play an important role for data transmission and neural signal propagation.

I am currently research fellow at the University of Leeds (UK) funded by URKI in recognition of a Horizon Europe MSCA award post Brexit. I have held research fellow positions at Northumbria University (UK), and jointly at the University of Auckland and the Dodd-Walls Centre for Photonic and Quantum Technologies (NZ). I obtained my doctoral degree from Technical University Berlin (DE) under the supervision of Serhiy Yanchuk. I was co-supervised by Tiago Pereira  at the University of Sao Paulo (BR). During my doctoral studies, I was a member of GRF International Research Training group 1740 (Dynamical phenomena in complex networks: Fundamentals and Applications) and GRF Collaborative Research Center  910 (Control of self-organizing nonlinear systems: Theoretical methods and concepts of applications).

Publications

Peer-reviewed publications:

1. Stefan Ruschel and Andrus Giraldo. Master stability for traveling waves on networks. Physical Review Letters, 134(25):257201 (2025) [Link][Arxiv]

2. Stefan Ruschel, Venkata A Pammi, Rémy Braive, Isabelle Sagnes, Grégoire Beaudoin, Neil GR Broderick, Bernd Krauskopf, and Sylvain Barbay. Regenerative vectorial breathers in a delay-coupled excitable microlaser with integrated saturable absorber. Optics Letters, 50(8):2618–2621 (2025)

3. Stefan Ruschel and Benoit Huard. A delay dynamical system’s perspective on the glucose–insulin regulatory response to on–off glucose infusion. The ANZIAM Journal, 67:e26 (2025) [Link][Arxiv]

4. A Giraldo, S Ruschel. Pulse-adding of Temporal Dissipative Solitons: Resonant Homoclinic Points and the Orbit Flip of Case B with Delay. Nonlinearity 36 (12), 7105 (2023) [Link][Arxiv]

5. AR Humphries, B Krauskopf, S Ruschel, J Sieber. Interplay between instantaneous and delayed feedback with delayed state dependence, Discr. Cont. Dyn. Sys. B (2022) [Link][Arxiv]

6. S Ruschel, S Yanchuk. The Spectrum of Delay Differential Equations with Multiple Hierarchical Large Delays, Discrete Cont. Dyn-S 14 (1), 151-175 (2021). [Link][Arxiv]

7. S Ruschel, B Krauskopf, NGR Broderick. The limits of sustained self-excitation and stable periodic pulse trains in the Yamada model with delayed optical feedback, Chaos 30 (9), 093101 (2020). [Link][Arxiv]

8. S Yanchuk, S Ruschel, J Sieber, M Wolfrum. Temporal dissipative solitons in time-delay feedback systems, Phys. Rev. Lett. 123 (5), 053901 (2019). [Link][Arxiv]

9. LS Young, S Ruschel, S Yanchuk, T Pereira. Consequences of delays and imperfect implementation of isolation in epidemic control, Sci Rep. 9, 3505 (2019). [Link][Arxiv]

10. S Ruschel, T Pereira, L-S Young, S Yanchuk. An SIQ delay differential equations model for disease control via isolation, J. Math. Biol., 79(1), 249-279 (2019). [Link][Arxiv]

11. S Ruschel, S Yanchuk. Delay-Induced Switched States in a slow-fast system, Phil. Trans. R. Soc. A. 377, 20180118 (2019). [Link][Arxiv]

12. IA Shepelev, AV Bukh, S Ruschel, S Yanchuk, TE Vadivasova. Local sensitivity of spatiotemporal structures, Nonlinear Dynamics 94(2), 1019–1027 (2018). [Link][Arxiv]

13. S Ruschel, S Yanchuk. Chaotic bursting in semiconductor lasers, Chaos 27, 114313 (2017). [Link][Arxiv]

Thesis:

14. S Ruschel. Multiple time-scale delay systems in mathematical biology and laser dynamics, doctoral thesis, Technische Universität Berlin (2020). [Link][Arxiv]

Preprints:

15. Stefan Ruschel, Sylvain Barbay, Neil GR Broderick, and Bernd Krauskopf. Strongly resonant polarization dynamics of pulse trains in a spin-flip model for an excitable microlaser with delayed self-feedback. arXiv preprint arXiv:2508.13630, 2025. [Link][Arxiv]

16. Renzo Mancini, Stefan Ruschel, Henk A. Dijkstra, and Bernd Krauskopf. Bifurcation analysis of a two-delay model for the atlantic meridional overturning circulation. Preprint, University of Auckland, 2025. [Link][Arxiv]

Conference proceedings:

17. S Ruschel, VA Pammi, B Krauskopf, NGR Broderick, S Barbay. Nonlinear Optics and its Applications 2022, PC121430U (2022). [Link][Arxiv]

18. S Ruschel, B Krauskopf, NGR Broderick. Onset and termination of sustained pulsation. OSA Advanced Photonics Congress, NpW2E.2 (2020). [Link][Arxiv]