Publications
Preprints
- M. Engel, F. Hummel, C. Kuehn, N. Popovic, M. Ptashnyk, T. Zacharis, Geometric analysis of fast-slow PDEs with fold singularities via Galerkin discretisation, submitted.
Peer-Reviewed
2024
- N. Popovic, Z. Miao, The Effect of a Cut-Off on a Model of Invasion with Dispersive Variability, in "Proceedings of the Workshop on Topics in Multiple Time Scale Dynamics, Banff 2022", Contemp. Math., to appear (2024). Download revised preprint.
2023
- P. Kaklamanos, C. Kuehn, N. Popovic, M. Sensi,
Entry-exit functions in fast-slow systems with intersecting eigenvalues, J. Dynam. Differential Equations, https://doi.org/10.1007/s10884-023-10266-2 (2023). Download revised preprint.
- P. Kaklamanos, N. Popovic,
Complex oscillatory dynamics in a three-timescale El Niño Southern Oscillation model, Phys. D 449, 133740 (2023). Download revised preprint.
- P. Kaklamanos, N. Popovic, K.U. Kristiansen, Geometric singular perturbation analysis of the multiple-timescale Hodgkin-Huxley equations, SIAM J. Appl. Dyn. Syst. 22(3), 1552-1589 (2023). Download revised preprint.
2022
- T. Filatova, N. Popovic, R. Grima,
Modulation of nuclear and cytoplasmic mRNA fluctuations by time-dependent stimuli: analytical distributions, Math. Biosci. 347, 108828 (2022). Download revised preprint.
- P. Kaklamanos, N. Popovic, K.U. Kristiansen,
Bifurcations of mixed-mode oscillations in three-timescale systems: an extended prototypical example, Chaos 32, 013108 (2022). Download revised preprint. Editor's Pick.
- Y. Patsios, R. Huzak, P. de Maesschalck, N. Popovic, Jump-induced mixed-mode oscillations through piecewise affine maps, J. Math. Anal. Appl. 505(1), 125641 (2022). Download revised preprint.
2021
- F. Veerman, N. Popovic, C. Marr,
Parameter inference with analytical propagators for stochastic models of autoregulated gene expression, Int. J. Nonlinear Sci. Numer. Simul., https://doi.org/10.1515/ijnsns-2019-0258 (2021). Download revised preprint.
- T. Filatova, N. Popovic, R. Grima,
Statistics of Nascent and Mature RNA Fluctuations in a Stochastic Model of Transcriptional Initiation, Elongation, Pausing, and Termination, Bull. Math. Biol. 83(3),
https://doi.org/10.1007/s11538-020-00827-7 (2021). Download
revised preprint.
- Z. Miao, N. Popovic, T. Zacharis, Geometric analysis of a two-body problem with quick loss of mass, Nonlinear Dyn. 104, 2015-2035 (2021). Download revised preprint.
2020
- Z. Miao, N. Popovic, P. Szmolyan, Oscillations in a cAMP signaling model for cell aggregation - a geometric analysis, J. Math. Anal. Appl. 483(1), 123577 (2020). Download revised preprint.
2019
- A. Iuorio, N. Popovic, P. Szmolyan, Singular perturbation analysis of a regularized MEMS model, SIAM J. Appl. Dyn. Syst. 18(2), 661-708 (2019). Download revised preprint.
2017
- F. Veerman, C. Marr, N. Popovic, Time-dependent propagators for stochastic models of gene expression: an analytical method, J. Math. Biol.,
https://doi.org/10.1007/s00285-017-1196-4 (2017). Download
revised preprint.
- M. Holzer, N. Popovic, Wavetrain solutions of a reaction-diffusion-advection model of mussel-algae interaction, SIAM J. Appl. Dyn. Syst. 16(1), 431-478 (2017). Download revised preprint.
2016
- N. Popovic, C. Marr, P.S. Swain,
A geometric analysis of fast-slow models for stochastic gene expression,
J. Math. Biol. 72(1), 87-122 (2016). Download
revised preprint; download
supplementary material.
- P. de Maesschalck, E. Kutafina, N. Popovic, Sector-Delayed-Hopf-Type Mixed-Mode Oscillations in a Prototypical Three-Time-Scale Model, Appl. Math. Comput. 273, 337-352 (2016). Download revised preprint.
2015
- J. Feigelman, C. Marr, N. Popovic, A Case Study on the Use of Scale Separation-Based Analytic Propagators for Parameter Inference in Stochastic Gene Regulation, J. Coupled Syst. Multiscale Dyn. 3(2), 164-173 (2015). Download revised preprint.
2014
- P. Thomas, C. Fleck, R. Grima, N. Popovic,
System size expansion using Feynman rules and diagrams,
J. Phys. A: Math. Theor. 47(45), 455007 (2014). Download
revised preprint.
- P. Thomas, N. Popovic, R. Grima,
Phenotypic switching in gene regulatory networks, Proc. Natl. Acad. Sci. USA
111(19), 6994-6999 (2014). Download
revised preprint; download
supplementary material.
- P. de Maesschalck, E. Kutafina, N. Popovic, Three time-scales in an extended Bonhoeffer-van der Pol oscillator, J. Dynam. Differential Equations 26(4), 955-987 (2014). Download revised preprint.
2013
- R. Basile, R. Grima, N. Popovic, A graph-based approach for the approximate solution of the Chemical Master Equation, Bull. Math. Biol. 75(10), 1653-1696 (2013). Download revised preprint.
2012
- N. Popovic,
A geometric analysis of front propagation in an integrable
Nagumo equation with a linear cut-off, Phys. D 241(22), 1976-1984 (2012).
Download revised preprint.
- P. de Maesschalck, N. Popovic, Gevrey properties of the asymptotic critical wave speed in a family of scalar reaction-diffusion equations, J. Math. Anal. Appl. 386(2), 542-558 (2012). Download revised preprint.
2011
- N. Popovic,
A Geometric Analysis of Front Propagation in a Family of Degenerate
Reaction-Diffusion Equations with Cut-Off,
Z. Angew. Math. Phys. 62(3), 405-437 (2011).
Download revised preprint.
- N. Popovic, A Geometric Classification of Traveling Front Propagation in the Nagumo Equation with Cut-Off, in "MURPHYS 2010: Proceedings of the International Workshop on Multi-Rate Processes and Hysteresis, Pecs, 2010", J. Phys. Conference Series 268, 012023 (2011). Download revised preprint.
2010
- F. Dumortier, N. Popovic, T.J. Kaper, A Geometric Approach to Bistable Front Propagation in Scalar Reaction-Diffusion Equations with Cut-Off, Phys. D 239(20-22), 1984-1999 (2010). Download revised preprint.
2009
- P. de Maesschalck, N. Popovic, T.J. Kaper,
Canards and Bifurcation Delays of Spatially Homogeneous and Inhomogeneous
Types in Reaction-Diffusion Equations,
Adv. Differential Equations 14(9-10), 943-962 (2009).
Download revised preprint.
- C. Burton, H. Knoop, N. Popovic, M. Sharpe, G. Bleijenberg, Reduced complexity of activity patterns in patients with Chronic Fatigue Syndrome: a case control study, BioPsychoSocial Medicine 3(7) (2009). Download revised preprint.
2008
- N. Popovic,
Mixed-Mode Dynamics and the Canard Phenomenon: Towards a Classification,
in "MURPHYS 2008: Proceedings of the International Workshop on Multi-Rate Processes
and Hysteresis, Cork 2008", J. Phys. Conference Series 138, 012020 (2008).
Download revised preprint.
- M. Krupa, N. Popovic, N. Kopell,
Mixed-Mode Oscillations in Three Time-Scale Systems: A
Prototypical Example.
SIAM J. Appl. Dyn. Syst. 7(2), 361-420 (2008).
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- G. van Baalen, N. Popovic, C.E. Wayne,
Long tails in the long time asymptotics of quasi-linear
hyperbolic-parabolic systems of conservation laws.
SIAM J. Math. Anal. 39(6), 1951-1977 (2008).
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- M. Krupa, N. Popovic, N. Kopell, H.G. Rotstein, Mixed-Mode Oscillations in a Three Time-Scale Model for the Dopaminergic Neuron, Chaos 18(1), 015106 (2008). Download revised preprint.
2007
- L.V. Kalachev, H.G. Kaper, T.J. Kaper, N. Popovic, A. Zagaris,
Reduction for Michaelis-Menten-Henri Kinetics in the
Presence of Diffusion,
in "Proceedings of the International Conference in Honor of Jacqueline Fleckinger,
Toulouse, France 2006", Electron. J. Differential Equations Conf. 16, 155-184 (2007).
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- N. Popovic,
Front Speeds, Cut-Offs, and Desingularization: A Brief Case Study,
in "Proceedings of the Conference on Fluids and Waves-Recent Trends in Applied
Analysis, Memphis 2006", Contemp. Math. 440, 187-195 (2007).
Download revised preprint.
- N. Popovic, D. Praetorius, A. Schlömerkemper,
Analysis and Numerical Simulation of Magnetic Forces between
Rigid Polygonal Bodies. Part I: Analysis,
Contin. Mech. Thermodyn. 19(1-2), 67-80 (2007).
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- N. Popovic, D. Praetorius, A. Schlömerkemper,
Analysis and Numerical Simulation of Magnetic Forces between
Rigid Polygonal Bodies. Part II: Numerical Simulation,
Contin. Mech. Thermodyn. 19(1-2), 81-109 (2007).
Download revised preprint.
- F. Dumortier, N. Popovic, T.J. Kaper,
The Critical Wave Speed for the Fisher-Kolmogorov-Petrowskii-Piscounov
Equation with Cut-Off,
Nonlinearity 20(4), 855-877 (2007).
Download revised preprint.
- F. Dumortier, N. Popovic, T.J. Kaper, The asymptotic critical wave speed in a family of scalar reaction-diffusion equations, J. Math. Anal. Appl. 326(2), 1007-1023 (2007). Download revised preprint.
2006
- N. Popovic, T.J. Kaper,
Rigorous asymptotic expansions for critical wave speeds in a
family of scalar reaction-diffusion equations,
J. Dynam. Differential Equations 18(1), 103-139 (2006).
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- N. Popovic, D. Praetorius, H-Matrix Techniques for Stray-Field Computations in Computational Micromagnetics, in "Large-Scale Scientific Computing: Proceedings of the 5th International Conference LSSC 2005, Sozopol, Bulgaria", Lecture Notes in Comput. Sci. 3743, 102-110 (2006). Download revised preprint.
2005
- N. Popovic, D. Praetorius, A. Schlömerkemper,
Magnetic Force Formulae for Magnets at Small Distances,
in "Proceedings of the GAMM Annual Meeting 2005, Luxembourg",
Proc. Appl. Math. Mech. 5(1), 631-632 (2005).
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- N. Popovic,
A Geometric Analysis of Logarithmic Switchback Phenomena,
in "HAMSA 2004: Proceedings of the International Workshop
on Hysteresis and Multi-Scale Asymptotics, Cork 2004", J. Phys. Conference
Series 22, 164-173 (2005).
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- N. Popovic, D. Praetorius,
Applications of H-Matrix Techniques in Micromagnetics,
Computing 74(3), 177-204 (2005).
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- N. Popovic, A Geometric Analysis of the Lagerstrom Model: Existence of Solutions and Rigorous Asymptotic Expansions, in "Equadiff 2003: Proceedings of the International Conference on Differential Equations, Hasselt 2003", 916-918 (2005). Download revised preprint.
2004
- N. Popovic, P. Szmolyan,
Rigorous asymptotic expansions for Lagerstrom's model
equation - a geometric approach,
Nonlinear Anal. 59(4), 531-565 (2004).
Download revised preprint.
- N. Popovic, P. Szmolyan, A geometric analysis of the Lagerstrom model problem, J. Differential Equations 199(2), 290-325 (2004). Download revised preprint.
Theses
2002
- N. Popovic, A Geometric Analysis of the Lagerstrom Model: Existence of Solutions and Rigorous Asymptotic Expansions, PhD Thesis, Vienna University of Technology, Vienna, Austria, 2002.
2000
- N. Popovic, Geometric Aspects of WKB Approximation: A Dynamical Systems Approach for the One-Dimensional Stationary Schrödinger Equation, Master's Thesis, Vienna University of Technology, Vienna, Austria, 2000.
Preprints have been revised in accordance with peer reviewers' reports; moreover, typographical errors and other minor mistakes have been corrected where appropriate.