School of Mathematical Sciences
 

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Stefan Ruschel

Research Associate/Fellow,

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Biography

I am currently a postdoctoral research fellow at the University of Nottingham, where I work with Rachel Nicks and Stephen Coombes on the Leverhulme funded project "White Matter Computation: Utilising axonal delays to sculpt network attractors". From 2024-25, I was Marie Slodowska Curie Postdoctoral Fellow (funded by URKI) at the University of Leeds. Previously, I was a research fellow at Northumbria University, Newcastle, and jointly at the University of Auckland and the Dodd-Walls Centre for Photonic and Quantum Technologies (NZ). I obtained my doctoral degree in 2019 from Technical University Berlin under the supervision of Serhiy Yanchuk. During my PhD was co-supervised by Tiago Pereira at the University of Sao Paulo. 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).

Expertise Summary

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. Some of my specific contributions involve the fixed point spectrum for large delay, as well as the characterization of traveling pulses and waves. My future research is dedicated to applying these techniques to network 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.

Selected Publications

  • RUSCHEL, STEFAN and GIRALDO, ANDRUS, 2025. Master Stability for Traveling Waves on Networks Physical Review Letters. 134(25), 257201
  • RUSCHEL, STEFAN, PAMMI, VENKATA A, BRAIVE, RÉMY, SAGNES, ISABELLE, BEAUDOIN, GRÉGOIRE, BRODERICK, NEIL GR, KRAUSKOPF, BERND and BARBAY, SYLVAIN, 2025. Regenerative vectorial breathers in a delay-coupled excitable microlaser with integrated saturable absorber Optics Letters. 50(8), 2618-2621
  • GIRALDO, ANDRUS and RUSCHEL, STEFAN, 2023. Pulse-adding of temporal dissipative solitons: Resonant homoclinic points and the orbit flip of case B with delay Nonlinearity. 36(12), 7105
  • HUMPHRIES, ANTONY R, KRAUSKOPF, BERND, RUSCHEL, STEFAN and SIEBER, JAN, 2022. Nonlinear effects of instantaneous and delayed state dependence in a delayed feedback loop Discrete and Continuous Dynamical Systems-B. 27(12), 7245-7273
  • RUSCHEL, STEFAN, BARBAY, SYLVAIN, BRODERICK, NEIL G. R. and KRAUSKOPF, BERND, 2025. Strongly resonant polarization dynamics of pulse trains in a spin-flip model for an excitable microlaser with delayed self-feedback European Physical Journal Special Topics. s11734-025
  • MANCINI, R, RUSCHEL, S, DIJKSTRA, H.A and KRAUSKOPF, B, 2025. Bifurcation analysis of a two-delay model for the Atlantic Meridional Overturning Circulation Preprint, University of Auckland.
  • RUSCHEL, STEFAN and HUARD, BENOIT, 2025. A delay dynamical systems perspective on the glucose-insulin regulatory response to on-off glucose infusion The ANZIAM Journal. 67, e26
  • RUSCHEL, STEFAN and GIRALDO, ANDRUS, 2025. Master Stability for Traveling Waves on Networks Physical Review Letters. 134(25), 257201
  • RUSCHEL, STEFAN, PAMMI, VENKATA A, BRAIVE, RÉMY, SAGNES, ISABELLE, BEAUDOIN, GRÉGOIRE, BRODERICK, NEIL GR, KRAUSKOPF, BERND and BARBAY, SYLVAIN, 2025. Regenerative vectorial breathers in a delay-coupled excitable microlaser with integrated saturable absorber Optics Letters. 50(8), 2618-2621
  • GIRALDO, ANDRUS and RUSCHEL, STEFAN, 2023. Pulse-adding of temporal dissipative solitons: Resonant homoclinic points and the orbit flip of case B with delay Nonlinearity. 36(12), 7105
  • RUSCHEL, STEFAN, PAMMI, VENKATA ANIRUDH, KRAUSKOPF, BERND, BRODERICK, NEIL GR and BARBAY, SYLVAIN, 2022. Polarization symmetry breaking of regenerative pulses in excitable microlasers with delayed optical feedback In: Nonlinear Optics and its Applications 2022. PC121430U
  • HUMPHRIES, ANTONY R, KRAUSKOPF, BERND, RUSCHEL, STEFAN and SIEBER, JAN, 2022. Nonlinear effects of instantaneous and delayed state dependence in a delayed feedback loop Discrete and Continuous Dynamical Systems-B. 27(12), 7245-7273
  • RUSCHEL, STEFAN and YANCHUK, SERHIY, 2021. The spectrum of delay differential equations with multiple hierarchical large delays Discrete & Continuous Dynamical Systems - S. 14(1), 151-175
  • RUSCHEL, STEFAN, KRAUSKOPF, BERND and BRODERICK, NEIL GR, 2020. Onset and termination of sustained pulsation in an excitable microlaser with optical feedback In: Nonlinear Photonics. NpW2E-2
  • RUSCHEL, STEFAN, KRAUSKOPF, BERND and BRODERICK, NEIL G. R., 2020. The limits of sustained self-excitation and stable periodic pulse trains in the Yamada model with delayed optical feedback Chaos: An Interdisciplinary Journal of Nonlinear Science. 30(9), 093101
  • YANCHUK, SERHIY, RUSCHEL, STEFAN, SIEBER, JAN and WOLFRUM, MATTHIAS, 2019. Temporal Dissipative Solitons in Time-Delay Feedback Systems Physical Review Letters. 123(5), 053901
  • RUSCHEL, STEFAN and YANCHUK, SERHIY, 2019. Delay-induced switched states in a slow-fast system Philosophical Transactions of the Royal Society A. 377, 20180118
  • RUSCHEL, STEFAN, PEREIRA, TIAGO, YANCHUK, SERHIY and YOUNG, LAI-SANG, 2019. An SIQ delay differential equations model for disease control via isolation Journal of Mathematical Biology. 79(1), 249-279
  • YOUNG, LAI-SANG, RUSCHEL, STEFAN, YANCHUK, SERHIY and PEREIRA, TIAGO, 2019. Consequences of delays and imperfect implementation of isolation in epidemic control Scientific Reports. 9, 3505
  • SHEPELEV, IGOR A, BUKH, ANDREI V, RUSCHEL, STEFAN, YANCHUK, SERHIY and VADIVASOVA, TATIANA E, 2018. Local sensitivity of spatiotemporal structures Nonlinear Dynamics. 94(2), 1019-1027
  • RUSCHEL, STEFAN and YANCHUK, SERHIY, 2017. Chaotic bursting in semiconductor lasers Chaos: An Interdisciplinary Journal of Nonlinear Science. 27(11), 114313

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