Jelbart, S.; Kuehn, C.; Kuntz, S.-V. Geometric blow-up for folded limit cycle manifolds in three time-scale systems. (English) Zbl 07787309 J. Nonlinear Sci. 34, No. 1, Paper No. 17, 68 p. (2024). MSC: 34E10 34E13 34E15 34E20 34C45 34C27 34C05 34C23 PDFBibTeX XMLCite \textit{S. Jelbart} et al., J. Nonlinear Sci. 34, No. 1, Paper No. 17, 68 p. (2024; Zbl 07787309) Full Text: DOI arXiv OA License
Jelbart, Samuel; Kuehn, Christian Discrete geometric singular perturbation theory. (English) Zbl 07688141 Discrete Contin. Dyn. Syst. 43, No. 1, 57-120 (2023). MSC: 39A12 34D15 34E15 34E20 34C45 34B16 PDFBibTeX XMLCite \textit{S. Jelbart} and \textit{C. Kuehn}, Discrete Contin. Dyn. Syst. 43, No. 1, 57--120 (2023; Zbl 07688141) Full Text: DOI arXiv
Eichinger, Katharina; Gnann, Manuel V.; Kuehn, Christian Multiscale analysis for traveling-pulse solutions to the stochastic FitzHugh-Nagumo equations. (English) Zbl 1501.35114 Ann. Appl. Probab. 32, No. 5, 3229-3282 (2022). MSC: 35C07 35K57 35R60 60H15 35Q92 PDFBibTeX XMLCite \textit{K. Eichinger} et al., Ann. Appl. Probab. 32, No. 5, 3229--3282 (2022; Zbl 1501.35114) Full Text: DOI arXiv
Engel, Maximilian; Kuehn, Christian; de Rijk, Björn A traveling wave bifurcation analysis of turbulent pipe flow. (English) Zbl 1506.34072 Nonlinearity 35, No. 11, 5903-5937 (2022). MSC: 34E15 34C23 34C37 35C07 37C29 37N10 76D05 76F06 PDFBibTeX XMLCite \textit{M. Engel} et al., Nonlinearity 35, No. 11, 5903--5937 (2022; Zbl 1506.34072) Full Text: DOI arXiv
Kuehn, Christian; Berglund, Nils; Bick, Christian; Engel, Maximilian; Hurth, Tobias; Iuorio, Annalisa; Soresina, Cinzia A general view on double limits in differential equations. (English) Zbl 1501.34001 Physica D 431, Article ID 133105, 26 p. (2022). MSC: 34-02 34E15 34E13 60H10 34F05 34C15 PDFBibTeX XMLCite \textit{C. Kuehn} et al., Physica D 431, Article ID 133105, 26 p. (2022; Zbl 1501.34001) Full Text: DOI arXiv
Engel, Maximilian; Kuehn, Christian; Petrera, Matteo; Suris, Yuri Discretized fast-slow systems with canards in two dimensions. (English) Zbl 1484.39016 J. Nonlinear Sci. 32, No. 2, Paper No. 19, 41 p. (2022). Reviewer: Jörg Härterich (Bochum) MSC: 39A28 39A12 34E15 34E20 37M15 37M20 37M21 37G10 65L06 PDFBibTeX XMLCite \textit{M. Engel} et al., J. Nonlinear Sci. 32, No. 2, Paper No. 19, 41 p. (2022; Zbl 1484.39016) Full Text: DOI arXiv
Jardón-Kojakhmetov, Hildeberto; Kuehn, Christian A survey on the blow-up method for fast-slow systems. (English) Zbl 1506.34003 Galaz-García, Fernando (ed.) et al., Mexican mathematicians in the world. Trends and recent contributions. IV meeting. Reunión de matemáticos mexicanos en el mundo, Casa Matemática Oaxaca, Oaxaca, Mexico, June 10–15, 2018. Providence, RI: American Mathematical Society (AMS); México: Sociedad Matemática Mexicana. Contemp. Math. 775, 115-160 (2021). MSC: 34-02 34E15 34C05 34E17 34A26 PDFBibTeX XMLCite \textit{H. Jardón-Kojakhmetov} and \textit{C. Kuehn}, Contemp. Math. 775, 115--160 (2021; Zbl 1506.34003) Full Text: DOI arXiv
Kuehn, Christian; Lux, Kerstin Uncertainty quantification of bifurcations in random ordinary differential equations. (English) Zbl 1484.34142 SIAM J. Appl. Dyn. Syst. 20, No. 4, 2295-2334 (2021). MSC: 34F10 34C23 60H35 41A58 44A15 34C45 PDFBibTeX XMLCite \textit{C. Kuehn} and \textit{K. Lux}, SIAM J. Appl. Dyn. Syst. 20, No. 4, 2295--2334 (2021; Zbl 1484.34142) Full Text: DOI arXiv
Gonzalez Herrero, Maria Elena; Kuehn, Christian; Tsaneva-Atanasova, Krasimira Reduced models of cardiomyocytes excitability: comparing Karma and FitzHugh-Nagumo. (English) Zbl 1468.92029 Bull. Math. Biol. 83, No. 8, Paper No. 88, 37 p. (2021). MSC: 92C37 35C07 35B25 PDFBibTeX XMLCite \textit{M. E. Gonzalez Herrero} et al., Bull. Math. Biol. 83, No. 8, Paper No. 88, 37 p. (2021; Zbl 1468.92029) Full Text: DOI arXiv
Breden, Maxime; Kuehn, Christian; Soresina, Cinzia On the influence of cross-diffusion in pattern formation. (English) Zbl 1469.35202 J. Comput. Dyn. 8, No. 2, 213-240 (2021). MSC: 35Q92 92D25 92C15 35B32 35B35 35K59 65P30 PDFBibTeX XMLCite \textit{M. Breden} et al., J. Comput. Dyn. 8, No. 2, 213--240 (2021; Zbl 1469.35202) Full Text: DOI arXiv
Jardón-Kojakhmetov, Hildeberto; Kuehn, Christian; Pugliese, Andrea; Sensi, Mattia A geometric analysis of the SIR, SIRS and SIRWS epidemiological models. (English) Zbl 1469.34065 Nonlinear Anal., Real World Appl. 58, Article ID 103220, 27 p. (2021). Reviewer: Xiang-Sheng Wang (Lafayette) MSC: 34C60 34E15 34C23 92D30 PDFBibTeX XMLCite \textit{H. Jardón-Kojakhmetov} et al., Nonlinear Anal., Real World Appl. 58, Article ID 103220, 27 p. (2021; Zbl 1469.34065) Full Text: DOI arXiv
Kuehn, Christian; Soresina, Cinzia Numerical continuation for a fast-reaction system and its cross-diffusion limit. (English) Zbl 1451.35237 SN Partial Differ. Equ. Appl. 1, No. 2, Paper No. 7, 26 p. (2020). MSC: 35Q92 70K70 35K59 65P30 PDFBibTeX XMLCite \textit{C. Kuehn} and \textit{C. Soresina}, SN Partial Differ. Equ. Appl. 1, No. 2, Paper No. 7, 26 p. (2020; Zbl 1451.35237) Full Text: DOI arXiv
Iuorio, Annalisa; Kuehn, Christian; Szmolyan, Peter Geometry and numerical continuation of multiscale orbits in a nonconvex variational problem. (English) Zbl 1434.70055 Discrete Contin. Dyn. Syst., Ser. S 13, No. 4, 1269-1290 (2020). MSC: 70K70 37G15 PDFBibTeX XMLCite \textit{A. Iuorio} et al., Discrete Contin. Dyn. Syst., Ser. S 13, No. 4, 1269--1290 (2020; Zbl 1434.70055) Full Text: DOI arXiv
Arcidiacono, Luca; Engel, Maximilian; Kuehn, Christian Discretized fast-slow systems near pitchfork singularities. (English) Zbl 1436.37062 J. Difference Equ. Appl. 25, No. 7, 1024-1051 (2019). Reviewer: Irina V. Konopleva (Ul’yanovsk) MSC: 37G10 37G05 37M20 37D10 70K70 65L12 PDFBibTeX XMLCite \textit{L. Arcidiacono} et al., J. Difference Equ. Appl. 25, No. 7, 1024--1051 (2019; Zbl 1436.37062) Full Text: DOI arXiv
Engel, Maximilian; Kuehn, Christian Discretized fast-slow systems near transcritical singularities. (English) Zbl 1416.37045 Nonlinearity 32, No. 7, 2365-2391 (2019). Reviewer: Robert Vrabel (Trnava) MSC: 37G10 37G15 37C05 70K70 65L06 65L12 65L11 PDFBibTeX XMLCite \textit{M. Engel} and \textit{C. Kuehn}, Nonlinearity 32, No. 7, 2365--2391 (2019; Zbl 1416.37045) Full Text: DOI arXiv
Kuehn, Christian; Romanò, Francesco; Kuhlmann, Hendrik C. Tracking particles in flows near invariant manifolds via balance functions. (English) Zbl 1398.70046 Nonlinear Dyn. 92, No. 3, 983-1000 (2018). MSC: 70K60 37N10 34D08 PDFBibTeX XMLCite \textit{C. Kuehn} et al., Nonlinear Dyn. 92, No. 3, 983--1000 (2018; Zbl 1398.70046) Full Text: DOI arXiv
Kuehn, Christian Uncertainty transformation via Hopf bifurcation in fast-slow systems. (English) Zbl 1404.37063 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2200, Article ID 20160346, 17 p. (2017). MSC: 37H20 34C23 34E13 PDFBibTeX XMLCite \textit{C. Kuehn}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2200, Article ID 20160346, 17 p. (2017; Zbl 1404.37063) Full Text: DOI arXiv
Kuehn, Christian Efficient gluing of numerical continuation and a multiple solution method for elliptic PDEs. (English) Zbl 1410.65480 Appl. Math. Comput. 266, 656-674 (2015). MSC: 65P30 65N30 35B32 35J25 35J61 PDFBibTeX XMLCite \textit{C. Kuehn}, Appl. Math. Comput. 266, 656--674 (2015; Zbl 1410.65480) Full Text: DOI arXiv
Kuehn, Christian; Szmolyan, Peter Multiscale geometry of the Olsen model and non-classical relaxation oscillations. (English) Zbl 1321.34065 J. Nonlinear Sci. 25, No. 3, 583-629 (2015). MSC: 34C60 92E20 34C26 34E13 34E15 34C45 34C23 PDFBibTeX XMLCite \textit{C. Kuehn} and \textit{P. Szmolyan}, J. Nonlinear Sci. 25, No. 3, 583--629 (2015; Zbl 1321.34065) Full Text: DOI arXiv
Berglund, Nils; Gentz, Barbara; Kuehn, Christian From random Poincaré maps to stochastic mixed-mode-oscillation patterns. (English) Zbl 1348.37087 J. Dyn. Differ. Equations 27, No. 1, 83-136 (2015). MSC: 37H20 60H10 60J10 37H10 34C10 PDFBibTeX XMLCite \textit{N. Berglund} et al., J. Dyn. Differ. Equations 27, No. 1, 83--136 (2015; Zbl 1348.37087) Full Text: DOI arXiv
Kuehn, Christian On decomposing mixed-mode oscillations and their return maps. (English) Zbl 1317.34058 Chaos 21, No. 3, 033107, 15 p. (2011). MSC: 34C15 34C10 34C20 34C60 34C23 PDFBibTeX XMLCite \textit{C. Kuehn}, Chaos 21, No. 3, 033107, 15 p. (2011; Zbl 1317.34058) Full Text: DOI arXiv Link
Kuehn, Christian A mathematical framework for critical transitions: bifurcations, fast-slow systems and stochastic dynamics. (English) Zbl 1225.35242 Physica D 240, No. 12, 1020-1035 (2011). Reviewer: Oleg V. Makeev (Ulyanovsk) MSC: 35Q84 82C31 PDFBibTeX XMLCite \textit{C. Kuehn}, Physica D 240, No. 12, 1020--1035 (2011; Zbl 1225.35242) Full Text: DOI arXiv
Kuehn, Christian From first Lyapunov coefficients to maximal canards. (English) Zbl 1193.34117 Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 5, 1467-1475 (2010). MSC: 34E17 34E15 34C23 34C20 PDFBibTeX XMLCite \textit{C. Kuehn}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 5, 1467--1475 (2010; Zbl 1193.34117) Full Text: DOI arXiv