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
Holzer, Matt; Kearney, Matthew; Molseed, Samuel; Tuttle, Katie; Wigginton, David Pushed fronts in a Fisher-KPP-Burgers system using geometric desingularization. (English) Zbl 07771606 NoDEA, Nonlinear Differ. Equ. Appl. 31, No. 1, Paper No. 2, 20 p. (2024). MSC: 35C07 35B25 35K57 34E15 PDFBibTeX XMLCite \textit{M. Holzer} et al., NoDEA, Nonlinear Differ. Equ. Appl. 31, No. 1, Paper No. 2, 20 p. (2024; Zbl 07771606) Full Text: DOI arXiv
Kristiansen, K. U. Blowup analysis of a hysteresis model based upon singular perturbations. (English) Zbl 07765723 J. Nonlinear Sci. 34, No. 1, Paper No. 6, 64 p. (2024). MSC: 34A36 34E15 34E17 34C23 34C55 PDFBibTeX XMLCite \textit{K. U. Kristiansen}, J. Nonlinear Sci. 34, No. 1, Paper No. 6, 64 p. (2024; Zbl 07765723) 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
Carmona, V.; Fernández-García, S.; Teruel, A. E. Birth, transition and maturation of canard cycles in a piecewise linear system with a flat slow manifold. (English) Zbl 1517.34083 Physica D 443, Article ID 133566, 16 p. (2023). Reviewer: Renato Huzak (Hasselt) MSC: 34E17 34A36 34A30 34E15 34C23 PDFBibTeX XMLCite \textit{V. Carmona} et al., Physica D 443, Article ID 133566, 16 p. (2023; Zbl 1517.34083) Full Text: DOI
Armbruster, Ashley; Holzer, Matt; Roselli, Noah; Underwood, Lena Epidemic spreading on complex networks as front propagation into an unstable state. (English) Zbl 1505.92185 Bull. Math. Biol. 85, No. 1, Paper No. 4, 28 p. (2023). MSC: 92D30 93C42 35Q92 PDFBibTeX XMLCite \textit{A. Armbruster} et al., Bull. Math. Biol. 85, No. 1, Paper No. 4, 28 p. (2023; Zbl 1505.92185) Full Text: DOI arXiv
Huzak, R.; Kristiansen, K. Uldall The number of limit cycles for regularized piecewise polynomial systems is unbounded. (English) Zbl 1512.34073 J. Differ. Equations 342, 34-62 (2023). Reviewer: Kuilin Wu (Guiyang) MSC: 34C07 34A36 34E15 34E17 34C05 34C23 PDFBibTeX XMLCite \textit{R. Huzak} and \textit{K. U. Kristiansen}, J. Differ. Equations 342, 34--62 (2023; Zbl 1512.34073) Full Text: DOI arXiv
Jelbart, S.; Kristiansen, K. U.; Szmolyan, P.; Wechselberger, M. Singularly perturbed oscillators with exponential nonlinearities. (English) Zbl 1505.34087 J. Dyn. Differ. Equations 34, No. 3, 1823-1875 (2022). MSC: 34E15 34C15 34C05 34C26 34C20 34A36 PDFBibTeX XMLCite \textit{S. Jelbart} et al., J. Dyn. Differ. Equations 34, No. 3, 1823--1875 (2022; Zbl 1505.34087) Full Text: DOI arXiv
Zhao, Liang; Shen, Jianhe Relaxation oscillations in a slow-fast predator-prey model with weak Allee effect and Holling-IV functional response. (English) Zbl 1487.92031 Commun. Nonlinear Sci. Numer. Simul. 112, Article ID 106517, 19 p. (2022). MSC: 92D25 34D23 PDFBibTeX XMLCite \textit{L. Zhao} and \textit{J. Shen}, Commun. Nonlinear Sci. Numer. Simul. 112, Article ID 106517, 19 p. (2022; Zbl 1487.92031) Full Text: DOI
Jelbart, Samuel; Pages, Nathan; Kirk, Vivien; Sneyd, James; Wechselberger, Martin Process-oriented geometric singular perturbation theory and calcium dynamics. (English) Zbl 1497.34060 SIAM J. Appl. Dyn. Syst. 21, No. 2, 982-1029 (2022). MSC: 34C15 34C26 34E15 92C37 34E13 93B30 PDFBibTeX XMLCite \textit{S. Jelbart} et al., SIAM J. Appl. Dyn. Syst. 21, No. 2, 982--1029 (2022; Zbl 1497.34060) 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
Kristiansen, Kristian U. A stiction oscillator under slowly varying forcing: uncovering small scale phenomena using blowup. (English) Zbl 1501.34020 SIAM J. Appl. Dyn. Syst. 20, No. 4, 2359-2390 (2021). MSC: 34A36 34C15 34E15 34C25 34E17 34C28 37N15 70E18 70K40 70F40 PDFBibTeX XMLCite \textit{K. U. Kristiansen}, SIAM J. Appl. Dyn. Syst. 20, No. 4, 2359--2390 (2021; Zbl 1501.34020) Full Text: DOI arXiv
Jelbart, Samuel; Kristiansen, Kristian Uldall; Wechselberger, Martin Singularly perturbed boundary-focus bifurcations. (English) Zbl 1472.34109 J. Differ. Equations 296, 412-492 (2021). MSC: 34E15 34A36 34C20 34C05 34C23 34C26 PDFBibTeX XMLCite \textit{S. Jelbart} et al., J. Differ. Equations 296, 412--492 (2021; Zbl 1472.34109) Full Text: DOI arXiv
Uldall Kristiansen, K.; Szmolyan, P. Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit. (English) Zbl 1477.34074 Nonlinearity 34, No. 2, 1030-1083 (2021). Reviewer: Robert Vrabel (Trnava) MSC: 34C60 92C45 34E15 34C26 34E17 PDFBibTeX XMLCite \textit{K. Uldall Kristiansen} and \textit{P. Szmolyan}, Nonlinearity 34, No. 2, 1030--1083 (2021; Zbl 1477.34074) Full Text: DOI arXiv
Taghvafard, Hadi; Jardón-Kojakhmetov, Hildeberto; Szmolyan, Peter; Cao, Ming Geometric analysis of oscillations in the Frzilator model. (English) Zbl 1483.34067 J. Math. Anal. Appl. 495, No. 1, Article ID 124725, 35 p. (2021). Reviewer: Joan Torregrosa (Barcelona) MSC: 34C60 34E15 34C26 92C45 PDFBibTeX XMLCite \textit{H. Taghvafard} et al., J. Math. Anal. Appl. 495, No. 1, Article ID 124725, 35 p. (2021; Zbl 1483.34067) Full Text: DOI arXiv
Brechmann, Pia; Rendall, Alan D. Unbounded solutions of models for glycolysis. (English) Zbl 1457.92057 J. Math. Biol. 82, No. 1-2, Paper No. 1, 23 p. (2021). MSC: 92C40 34C11 37N25 PDFBibTeX XMLCite \textit{P. Brechmann} and \textit{A. D. Rendall}, J. Math. Biol. 82, No. 1--2, Paper No. 1, 23 p. (2021; Zbl 1457.92057) Full Text: DOI arXiv
Kristiansen, K. Uldall A new type of relaxation oscillation in a model with rate-and-state friction. (English) Zbl 1486.34112 Nonlinearity 33, No. 6, 2960-3037 (2020). MSC: 34E15 34A26 34C26 70K70 34C45 86A15 PDFBibTeX XMLCite \textit{K. U. Kristiansen}, Nonlinearity 33, No. 6, 2960--3037 (2020; Zbl 1486.34112) Full Text: DOI arXiv
Jelbart, Samuel; Wechselberger, Martin Two-stroke relaxation oscillators. (English) Zbl 1486.34111 Nonlinearity 33, No. 5, 2364-2408 (2020). MSC: 34E15 34E17 34C26 PDFBibTeX XMLCite \textit{S. Jelbart} and \textit{M. Wechselberger}, Nonlinearity 33, No. 5, 2364--2408 (2020; Zbl 1486.34111) Full Text: DOI arXiv
Kristiansen, K. Uldall The regularized visible fold revisited. (English) Zbl 1469.34029 J. Nonlinear Sci. 30, No. 6, 2463-2511 (2020); correction ibid. 33, No. 4, Paper No. 56, 7 p. (2023); correction ibid. 34, No. 1, Paper No. 1, 1 p. (2024). MSC: 34A36 34E15 34C05 34C20 34C23 PDFBibTeX XMLCite \textit{K. U. Kristiansen}, J. Nonlinear Sci. 30, No. 6, 2463--2511 (2020; Zbl 1469.34029) 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
Kristiansen, Kristian Uldall Geometric singular perturbation analysis of a dynamical target mediated drug disposition model. (English) Zbl 1417.92065 J. Math. Biol. 79, No. 1, 187-222 (2019). MSC: 92C45 92C50 34E15 PDFBibTeX XMLCite \textit{K. U. Kristiansen}, J. Math. Biol. 79, No. 1, 187--222 (2019; Zbl 1417.92065) Full Text: DOI Link
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
Hasan, Cris R.; Krauskopf, Bernd; Osinga, Hinke M. Mixed-mode oscillations and twin canard orbits in an autocatalytic chemical reaction. (English) Zbl 1381.37107 SIAM J. Appl. Dyn. Syst. 16, No. 4, 2165-2195 (2017). MSC: 37N25 34E15 34E17 37M20 37G25 65L10 92E20 PDFBibTeX XMLCite \textit{C. R. Hasan} et al., SIAM J. Appl. Dyn. Syst. 16, No. 4, 2165--2195 (2017; Zbl 1381.37107) Full Text: DOI
Bossolini, Elena; Brøns, Morten; Kristiansen, Kristian Uldall Singular limit analysis of a model for earthquake faulting. (English) Zbl 1381.34067 Nonlinearity 30, No. 7, 2805-2834 (2017). Reviewer: Nikola Popovic (Edinburgh) MSC: 34C60 34E15 34C26 86A17 34C23 PDFBibTeX XMLCite \textit{E. Bossolini} et al., Nonlinearity 30, No. 7, 2805--2834 (2017; Zbl 1381.34067) Full Text: DOI arXiv
Holzer, Matt; Popović, Nikola Wavetrain solutions of a reaction-diffusion-advection model of mussel-algae interaction. (English) Zbl 1434.35256 SIAM J. Appl. Dyn. Syst. 16, No. 1, 431-478 (2017). MSC: 35Q92 35B36 35C07 35K57 35M30 PDFBibTeX XMLCite \textit{M. Holzer} and \textit{N. Popović}, SIAM J. Appl. Dyn. Syst. 16, No. 1, 431--478 (2017; Zbl 1434.35256) Full Text: DOI
Huzak, Renato Regular and slow-fast codimension 4 saddle-node bifurcations. (English) Zbl 1365.34070 J. Differ. Equations 262, No. 2, 1119-1154 (2017). Reviewer: Jörg Härterich (Bochum) MSC: 34C23 34E15 37G15 34E20 34C26 34C05 PDFBibTeX XMLCite \textit{R. Huzak}, J. Differ. Equations 262, No. 2, 1119--1154 (2017; Zbl 1365.34070) Full Text: DOI
Hayes, Michael G.; Kaper, Tasso J.; Szmolyan, Peter; Wechselberger, Martin Geometric desingularization of degenerate singularities in the presence of fast rotation: A new proof of known results for slow passage through Hopf bifurcations. (English) Zbl 1380.37105 Indag. Math., New Ser. 27, No. 5, 1184-1203 (2016). Reviewer: Valery A. Gaiko (Minsk) MSC: 37G15 34E15 37C45 34C23 PDFBibTeX XMLCite \textit{M. G. Hayes} et al., Indag. Math., New Ser. 27, No. 5, 1184--1203 (2016; Zbl 1380.37105) Full Text: DOI
Kosiuk, Ilona; Szmolyan, Peter Geometric analysis of the Goldbeter minimal model for the embryonic cell cycle. (English) Zbl 1344.34068 J. Math. Biol. 72, No. 5, 1337-1368 (2016). Reviewer: Nikola Popovic (Edinburgh) MSC: 34E15 34C20 34C26 34E13 92C37 92C45 34C60 34C45 PDFBibTeX XMLCite \textit{I. Kosiuk} and \textit{P. Szmolyan}, J. Math. Biol. 72, No. 5, 1337--1368 (2016; Zbl 1344.34068) Full Text: DOI
Manukian, Vahagn On travelling waves of the Gray-Scott model. (English) Zbl 1327.35181 Dyn. Syst. 30, No. 3, 270-296 (2015). MSC: 35K57 35B25 35B36 35B32 35C07 PDFBibTeX XMLCite \textit{V. Manukian}, Dyn. Syst. 30, No. 3, 270--296 (2015; Zbl 1327.35181) Full Text: DOI
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
Jardón-Kojakhmetov, H.; Broer, Henk W. Polynomial normal forms of constrained differential equations with three parameters. (English) Zbl 1305.34056 J. Differ. Equations 257, No. 4, 1012-1055 (2014). Reviewer: Werner M. Seiler (Kassel) MSC: 34C20 34A09 34A26 34E15 PDFBibTeX XMLCite \textit{H. Jardón-Kojakhmetov} and \textit{H. W. Broer}, J. Differ. Equations 257, No. 4, 1012--1055 (2014; Zbl 1305.34056) Full Text: DOI arXiv
Huzak, R.; De Maesschalck, P.; Dumortier, F. Limit cycles in slow-fast codimension 3 saddle and elliptic bifurcations. (English) Zbl 1316.34060 J. Differ. Equations 255, No. 11, 4012-4051 (2013). Reviewer: Christos Sourdis (Athens) MSC: 34E15 37G15 34E20 34C23 34C26 34C05 34C45 34C20 PDFBibTeX XMLCite \textit{R. Huzak} et al., J. Differ. Equations 255, No. 11, 4012--4051 (2013; Zbl 1316.34060) Full Text: DOI