Thibault-Greugny, E., Fages, F., Radulescu, O., Szmolyan, P., & Stamatas, G. N. (2024). A skin microbiome model with AMP interactions and analysis of quasi-stability vs stability in population dynamics. Theoretical Computer Science, 983, Article 114294. https://doi.org/10.1016/j.tcs.2023.114294 ( reposiTUm)
Kristiansen, K. U., & Szmolyan, P. (2024). A dynamical systems approach to WKB-methods: The simple turning point. Journal of Differential Equations, 406, 202–254. https://doi.org/10.1016/j.jde.2024.06.006 ( reposiTUm)
Iuorio, A., Jankowiak, G., Szmolyan, P., & Wolfram, M.-T. (2022). A PDE model for unidirectional flows: Stationary profiles and asymptotic behaviour. Journal of Mathematical Analysis and Applications, 510(2), Article 126018. https://doi.org/10.1016/j.jmaa.2022.126018 ( reposiTUm)
Uldall Kristiansen, K., & Szmolyan, P. (2021). Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit. Nonlinearity, 34(2), 1030–1083. https://doi.org/10.1088/1361-6544/abb542 ( reposiTUm)
Taghvafard, H., Jardón-Kojakhmetov, H., Szmolyan, P., & Cao, M. (2021). Geometric analysis of oscillations in the Frzilator model. Journal of Mathematical Analysis and Applications, 495(1), Article 124725. https://doi.org/10.1016/j.jmaa.2020.124725 ( reposiTUm)
Jelbart, S., Kristiansen, K. U., Szmolyan, P., & Wechselberger, M. (2021). Singularly Perturbed Oscillators with Exponential Nonlinearities. Journal of Dynamics and Differential Equations, 34(3), 1823–1875. https://doi.org/10.1007/s10884-021-10041-1 ( reposiTUm)
Iuorio, A., Kuehn, C., & Szmolyan, P. (2020). Geometry and numerical continuation of multiscale orbits in a nonconvex variational problem. Discrete and Continuous Dynamical Systems - Series S, 13(4), 1269–1290. https://doi.org/10.3934/dcdss.2020073 ( reposiTUm)
Miao, Z., Popović, N., & Szmolyan, P. (2020). Oscillations in a cAMP signaling model for cell aggregation - a geometric analysis. Journal of Mathematical Analysis and Applications, 483, Article 123577. https://doi.org/10.1016/j.jmaa.2019.123577 ( reposiTUm)
Iuorio, A., Popović, N., & Szmolyan, P. (2019). Singular perturbation analysis of a regularized MEMS mode. SIAM Journal on Applied Dynamical Systems, 18(2), 661–708. https://doi.org/10.1137/18m1197552 ( reposiTUm)
Hayes, M. G., Kaper, T. J., Szmolyan, P., & Wechselberger, M. (2016). Geometric desingularization of degenerate singularities in the presence of fast rotation: A new proof of known results for slow passage through Hopf bifurcations. Indagationes Mathematicae, 27(5), 1184–1203. https://doi.org/10.1016/j.indag.2015.11.005 ( reposiTUm)
Kosiuk, I., & Szmolyan, P. (2016). Geometric analysis of the Goldbeter minimal model for the embryonic cell cycle. Journal of Mathematical Biology, 72(5), 1337–1368. https://doi.org/10.1007/s00285-015-0905-0 ( reposiTUm)
Gasser, I., Szmolyan, P., & Wächtler, J. (2016). Existence of Chapman-Jouguet Detonation and Deflagration Waves. Journal of Mathematical Analysis and Applications, 48(2), 1400–1422. https://doi.org/10.1137/140985810 ( reposiTUm)
Kuehn, C., & Szmolyan, P. (2015). Multiscale geometry of the Olsen model and non-classical relaxation oscillations. Journal of Nonlinear Science, 25(3), 583–629. https://doi.org/10.1007/s00332-015-9235-z ( reposiTUm)
Freistühler, H., Szmolyan, P., & Wächtler, J. (2014). Spectral stability of shock waves associated with not genuinely nonlinear modes. Journal of Differential Equations, 257(1), 185–206. https://doi.org/10.1016/j.jde.2014.03.018 ( reposiTUm)
Freistühler, H., & Szmolyan, P. (2010). Spectral Stability of Small-Amplitude Viscous Shock Waves in Several Space Dimensions. Archive for Rational Mechanics and Analysis, 195(2), 353–373. https://doi.org/10.1007/s00205-009-0272-3 ( reposiTUm)
Schecter, S., & Szmolyan, P. (2009). Persistence of Rarefactions under Dafermos Regularization: Blow-Up and an Exchange Lemma for Gain-of-Stability Turning Points. SIAM Journal on Applied Dynamical Systems, 8(3), 822–853. https://doi.org/10.1137/080715305 ( reposiTUm)
Szmolyan, P., & Gucwa, I. (2009). Geometric singular perturbation analysis of an Autocatolotor model. Discrete and Continuous Dynamical Systems S, 2(4), 783–806. http://hdl.handle.net/20.500.12708/166636 ( reposiTUm)
Beiträge in Tagungsbänden
Szmolyan, P., Kristiansen, K. U., & Jelbart, S. I. (2024). Geometric analysis of Travelling Waves in the Zeldovich-Frank-Kamenetskii Equation. In Book of Abstracts: Equadiff 2024 (pp. 209–210). ( reposiTUm)
Jelbart, S. I., Martinez Sanchez, A., Kühn, C., & Szmolyan, P. (2024). Geometric Blow-up for Dynamic Bifurcations in Reaction-Diffusion Equations. In Book of Abstracts: Equadiff 2024 (pp. 206–207). http://hdl.handle.net/20.500.12708/199090 ( reposiTUm)
Desoeuvres, A., Szmolyan, P., & Radulescu, O. (2022). Qualitative Dynamics of Chemical Reaction Networks: An Investigation Using Partial Tropical Equilibrations. In Petre Ion & Păun Andrei (Eds.), Computational Methods in Systems Biology (pp. 61–85). Springer Cham. https://doi.org/10.1007/978-3-031-15034-0_4 ( reposiTUm)
Amirkhanov, A., Kosiuk, I., Szmolyan, P., Amirkhanov, A., Mistelbauer, G., Gröller, E., & Raidou, R. (2019). ManyLands: A Journey Across 4D Phase Space of Trajectories. In Eurographics journal, Computer Graphics Forum (CGF) Volume 38, Issue 7 (pp. 191–202). Eurographics journal, Computer Graphics Forum (CGF). http://hdl.handle.net/20.500.12708/57902 ( reposiTUm)
Szmolyan, P., Nipp, K., & Stoffer, D. (2009). Graph Transform and Blow-up in Singular Perturbations. In AIP Conference Proceedings. 7th International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2009), Rethymno, Kreta, Griechenland, EU. AIP Conference Proceedings. https://doi.org/10.1063/1.3241616 ( reposiTUm)
Präsentationen
Szmolyan, P., Kristiansen, K. U., Jelbart, S. I., & Baumgartner, L. (2024, July 9). What’s left to be done in GSPT ? [Presentation]. Workshop: Multiple scales: theory and applications 2024, Leiden, Netherlands (the). ( reposiTUm)
Baumgartner, L., & Szmolyan, P. (2024, July 8). A multi-parameter singular perturbation analysis of the Robertson model [Poster Presentation]. Workshop on Multiple scales: theory and applications (2024), Leiden, Netherlands (the). ( reposiTUm)
Szmolyan, P. (2024, September 26). Dynamics of Multi-Scale Systems [Presentation]. Science Day 2024, Graz, Austria. ( reposiTUm)
Baumgartner, L., & Szmolyan, P. (2024, December 17). A multi-parameter singular perturbation analysis of the Robertson model [Presentation]. Formal reaction kinetics and related questions 2024, Hungary. ( reposiTUm)
Szmolyan, P. (2023, October 27). Switching mechanisms in multiscale biological systems [Presentation]. Computing combinatorial dynamics in high dimensional biological networks, Leiden, Netherlands (the). ( reposiTUm)
Baumgartner, L., & Szmolyan, P. (2023, August 31). Robertson Model - A multi-parameter singular perturbation problem [Poster Presentation]. Universityof Groningen Summer School on Multiscale Modeling and its Applications, Netherlands (the). ( reposiTUm)
Szmolyan, P. (2019). Rescalings and blow-up in biochemical systems. Workshop on Reduction Methods for Chemical Reaction Networks, RWTH Aachen, Germany. http://hdl.handle.net/20.500.12708/123517 ( reposiTUm)
Szmolyan, P. (2019). Multiple time-scale dynamical systems in cell biology. Bioinspired Analysis of Dynamical Systems and Protein Network Analysis, Esztergom, Hungary. http://hdl.handle.net/20.500.12708/123508 ( reposiTUm)
Szmolyan, P. (2019). Advances in GSPT - teaching new tricks to an old dog? SIAM Conference on Applications of dynamical systems 2019, Snowbird, United States of America (the). http://hdl.handle.net/20.500.12708/123507 ( reposiTUm)
Szmolyan, P. (2018). Singular perturbations and slow-fast dynamics in chemical networks. Advances in Chemical Reaction Network Theory, Wien, Austria. http://hdl.handle.net/20.500.12708/123509 ( reposiTUm)
Szmolyan, P. (2017). Slow-fast systems: progress and challenges. The future of singular perturbations and the analysis of multiscale systems, Leiden, Netherlands (the). http://hdl.handle.net/20.500.12708/123512 ( reposiTUm)
Kuehn, C., & Szmolyan, P. (2014). Oscillations in multiple time scale dynamics: Autocatalysis, Koper, Olsen, and beyond. Rhythms in Complex Networks: From Theory to Experiment, Copenhagen, EU. http://hdl.handle.net/20.500.12708/120858 ( reposiTUm)
Kuehn, C., & Szmolyan, P. (2014). Non-Classical Relaxation Oscillations in the Olsen Model. Oberseminar Differentialgleichungen 08.05.2014, Augsburg, EU. http://hdl.handle.net/20.500.12708/120864 ( reposiTUm)
Kuehn, C., & Szmolyan, P. (2013). Two Examples of Geometric Desingularization of Nonstandard Systems. Workshop on Slow-Fast Dynamics: Theory, Numerics, Application to Life and Earth Sciences, Barcelona, EU. http://hdl.handle.net/20.500.12708/120483 ( reposiTUm)
Szmolyan, P. (2010). Spectral stability of small-amplitude viscous shock waves. Joint SIAM/RSME-SCM-SEMA Meeting Emerging Topics in Dynamical Systems and Partial Differential Equations DSPDEs’10, Barcelona, EU. http://hdl.handle.net/20.500.12708/119669 ( reposiTUm)
Szmolyan, P. (2010). Geometric singular perturbation theory beyond the standard form. Colloquium on dynamical systems, Comenius Universität, Bratislava, EU. http://hdl.handle.net/20.500.12708/119670 ( reposiTUm)
Szmolyan, P. (2010). Blow-up analysis of glycolytic relaxation oscillations. 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Dresden, EU. http://hdl.handle.net/20.500.12708/119667 ( reposiTUm)
Szmolyan, P. (2007). Geometric analysis of delayed Hopf bifurcations. International Conference on Topological Methods, Differential Equations, and Dynamical Systems, Florenz, EU. http://hdl.handle.net/20.500.12708/118543 ( reposiTUm)
Szmolyan, P. (2006). Spectral stability of viscous shock waves in several space dimensions. Ordinary Differential Equations, their Applications and Related Topics, Trento, Italien, EU. http://hdl.handle.net/20.500.12708/118114 ( reposiTUm)
Szmolyan, P. (2004). Geometric singular perturbation analysis of viscous shock waves. International Workshop on hysteresis and multiscale asymptotics, University College Cork (2004)., Cork, Austria. http://hdl.handle.net/20.500.12708/117240 ( reposiTUm)
Szmolyan, P. (2002). Spectral stability of small amplitude shock waves Spectral stability of small amplitude shock waves. Fourth international conference on dynamical systems and differential equations, Wilmington, N.C., USA, Austria. http://hdl.handle.net/20.500.12708/117245 ( reposiTUm)
Weinmüller, E., Ponweiser, K., Linzer, W., & Szmolyan, P. (1993). Numerical Simulation oof a Natural Circulation Steam Generator. International Conference on Scientific Computation and Differential Equations, Auckland, EU. http://hdl.handle.net/20.500.12708/120746 ( reposiTUm)
Berichte
Achleitner, F., & Szmolyan, P. (2010). Saddle-node bifurcation of viscous profiles (ASC Report 21/2010). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/26869 ( reposiTUm)
Gucwa, I., & Szmolyan, P. (2009). Scaling in singular perturbation problems: blowing-up a relaxation oscillator (ASC Report 39/2009). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/26482 ( reposiTUm)
Freistühler, H., & Szmolyan, P. (2008). Spectral stability of small-amplitude viscous shock waves in several space dimensions (ASC Report 28/2008). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/26120 ( reposiTUm)
Schecter, S., & Szmolyan, P. (2008). Rarefactions in the Dafermos regularization of a system of conservation laws (ASC Report 27/2008). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/26119 ( reposiTUm)
Gucwa, I., & Szmolyan, P. (2008). Geometric singular perturbation analysis of an autocatalator model (ASC Report 26/2008). Institute of Analysis and Scientific Computing, TU Wien. http://hdl.handle.net/20.500.12708/26118 ( reposiTUm)
Preprints
Jelbart, S. I., Uldall Kristiansen, K., & Szmolyan, P. (2024). Travelling Waves and Exponential Nonlinearities in the Zeldovich-Frank-Kamenetskii Equation. arXiv. https://doi.org/10.48550/arXiv.2405.10076 ( reposiTUm)
