Research
Publications
S. Jelbart & M. Wechselberger: Two-stroke relaxation oscillators. Nonlinearity 33, (2020), 2364–2408. arXiv:1905.06539.
S. Jelbart, K. U. Kristiansen & M. Wechselberger: Singularly perturbed boundary-focus bifurcations. Journal of Differential Equations 296, (2021), 412–492. arXiv:2006.06087.
S. Jelbart, K. U. Kristiansen, P. Szmolyan & M. Wechselberger: Singularly perturbed oscillators with exponential nonlinearities. Journal of Dynamics and Differential Equations 122, (2021), 1572-9222. arXiv:1912.11769.
S. Jelbart, K. U. Kristiansen & M. Wechselberger: Singularly perturbed boundary-equilibrium bifurcations. Nonlinearity 34, (2021), 7371. arXiv:2103.09613.
S. Jelbart, V. Kirk, N. Pages, J. Sneyd & M. Wechselberger: Process-oriented geometric singular perturbation theory and calcium dynamics. SIAM Journal on Applied Dynamical Systems 21.2, (2022), 982-1029. arXiv:2104.07304.
S. Jelbart & C. Kuehn: Discrete geometric singular perturbation theory. Discrete and Continuous Dynamical Systems A 43, (2023), 57-120. arXiv:2201.06996.
S. Jelbart, S. -V. Kuntz & C. Kuehn. Geometric blow-up for folded limit cycle manifolds in three time-scale systems. Journal of Nonlinear Science 34, (2024), no.17. arXiv:2208.01361.
S. Jelbart. Rate and bifurcation induced transitions in asymptotically slow-fast systems. SIAM Journal on Applied Dynamical Systems, 23.3, (2024), 1836-1869. arXiv:2401.08482.
S. Jelbart & C. Kuehn: A formal geometric blow-up method for pattern forming systems. To appear in AMS proceedings of the conference Topics in Multiple Time Scale Dynamics, (2024). arXiv:2302.06343.
Thesis
S. Jelbart. Beyond slow-fast: relaxation oscillations in singularly perturbed non-smooth systems. PhD thesis, The University of Sydney, (2020).
arXiv Preprints
F. Hummel, S. Jelbart & C. Kuehn. Geometric blow-up of a dynamic Turing instability in the Swift-Hohenberg equation. (2022). arXiv:2207.03967.
S. Jelbart & C. Kuehn. Extending discrete geometric singular perturbation theory to non-hyperbolic points. (2023). arXiv:2308.06141.
B. Rahmani, S. Jelbart, V. Kirk & J. Sneyd. Understanding broad-spike oscillations in a model of intracellular calcium dynamics. (2024). arXiv:2401.16839.
S. Jelbart, K. U. Kristiansen, P. Szmolyan: Travelling Waves and exponential nonlinearities in the Zeldovich-Frank-Kamenetskii equation, (2024). arXiv:2405.10076.
Current Projects
Geometric blow-up methods for PDEs. Collaborators: C. Kuehn, A. M. Sánchez, P. Szmolyan.
Geometric analysis and modelling of calcium oscillations. Collaborators: B. Rahmani, V. Kirk, J. Sneyd.
Geometric singular perturbation approaches to problems with singular exponential nonlinearities. Collaborators: K. U. Kristiansen, P. Szmolyan.
Multiscale and geometric methods for consensus networks. Collaborators: H. Jardón Kojakhmetov.