Chen, Hebai; Chen, Xingwu; Jia, Man; Tang, Yilei A quintic \(\mathbb{Z}_2\)-equivariant Liénard system arising from the complex Ginzburg-Landau equation. (English) Zbl 07763741 SIAM J. Math. Anal. 55, No. 6, 5993-6038 (2023). Reviewer: Qinlong Wang (Guilin) MSC: 34C05 34C14 34C20 34C23 34C37 PDFBibTeX XMLCite \textit{H. Chen} et al., SIAM J. Math. Anal. 55, No. 6, 5993--6038 (2023; Zbl 07763741) Full Text: DOI
Ambrosio, B. Qualitative analysis of certain reaction-diffusion systems of the FitzHugh-Nagumo type. (English) Zbl 1523.35205 Evol. Equ. Control Theory 12, No. 6, 1507-1526 (2023). MSC: 35K57 35K51 37G10 92B25 92C20 PDFBibTeX XMLCite \textit{B. Ambrosio}, Evol. Equ. Control Theory 12, No. 6, 1507--1526 (2023; Zbl 1523.35205) Full Text: DOI arXiv
Chen, Shuang; Duan, Jinqiao Instability of small-amplitude periodic waves from fold-Hopf bifurcation. (English) Zbl 1508.37101 J. Math. Phys. 63, No. 11, Article ID 112702, 18 p. (2022). MSC: 37L15 37L10 35K57 35C07 PDFBibTeX XMLCite \textit{S. Chen} and \textit{J. Duan}, J. Math. Phys. 63, No. 11, Article ID 112702, 18 p. (2022; Zbl 1508.37101) 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
Carter, Paul; Champneys, Alan R. Wiggly canards: growth of traveling wave trains through a family of fast-subsystem foci. (English) Zbl 1495.34082 Discrete Contin. Dyn. Syst., Ser. S 15, No. 9, 2433-2466 (2022). MSC: 34E17 34C23 37G15 35C07 PDFBibTeX XMLCite \textit{P. Carter} and \textit{A. R. Champneys}, Discrete Contin. Dyn. Syst., Ser. S 15, No. 9, 2433--2466 (2022; Zbl 1495.34082) Full Text: DOI
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
Shen, Jianhe; Zhang, Xiang Traveling pulses in a coupled FitzHugh-Nagumo equation. (English) Zbl 1492.34044 Physica D 418, Article ID 132848, 11 p. (2021). MSC: 34C37 34E15 35C07 92C37 35K57 PDFBibTeX XMLCite \textit{J. Shen} and \textit{X. Zhang}, Physica D 418, Article ID 132848, 11 p. (2021; Zbl 1492.34044) Full Text: DOI
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
Wang, Xianjun; Gu, Huaguang; Lu, Bo Big homoclinic orbit bifurcation underlying post-inhibitory rebound spike and a novel threshold curve of a neuron. (English) Zbl 1484.37054 Electron. Res. Arch. 29, No. 5, 2987-3015 (2021). MSC: 37G15 37N25 92B20 37C29 PDFBibTeX XMLCite \textit{X. Wang} et al., Electron. Res. Arch. 29, No. 5, 2987--3015 (2021; Zbl 1484.37054) Full Text: DOI
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
Carter, Paul; Rademacher, Jens D. M.; Sandstede, Björn Pulse replication and accumulation of eigenvalues. (English) Zbl 1490.35034 SIAM J. Math. Anal. 53, No. 3, 3520-3576 (2021). Reviewer: Anna Ghazaryan (Oxford) MSC: 35B35 35P15 35C07 35B25 37L15 34E17 35K58 PDFBibTeX XMLCite \textit{P. Carter} et al., SIAM J. Math. Anal. 53, No. 3, 3520--3576 (2021; Zbl 1490.35034) Full Text: DOI arXiv
Chen, Hebai; Zhu, Huaiping Global bifurcation studies of a cubic Liénard system. (English) Zbl 1464.34061 J. Math. Anal. Appl. 496, No. 2, Article ID 124810, 24 p. (2021). Reviewer: Chunrui Zhang (Harbin) MSC: 34C23 34A34 34L05 PDFBibTeX XMLCite \textit{H. Chen} and \textit{H. Zhu}, J. Math. Anal. Appl. 496, No. 2, Article ID 124810, 24 p. (2021; Zbl 1464.34061) Full Text: DOI
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
Barrio, R.; Ibáñez, S.; Pérez, L.; Serrano, S. Spike-adding structure in fold/hom bursters. (English) Zbl 1453.37080 Commun. Nonlinear Sci. Numer. Simul. 83, Article ID 105100, 15 p. (2020). MSC: 37N25 37M20 92B20 PDFBibTeX XMLCite \textit{R. Barrio} et al., Commun. Nonlinear Sci. Numer. Simul. 83, Article ID 105100, 15 p. (2020; Zbl 1453.37080) Full Text: DOI
Barrio, Roberto; Ibáñez, Santiago; Pérez, Lucía Homoclinic organization in the Hindmarsh-rose model: a three parameter study. (English) Zbl 1437.92021 Chaos 30, No. 5, 053132, 20 p. (2020). MSC: 92C20 34C60 PDFBibTeX XMLCite \textit{R. Barrio} et al., Chaos 30, No. 5, 053132, 20 p. (2020; Zbl 1437.92021) Full Text: DOI
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
Carter, Paul; Doelman, Arjen Traveling stripes in the Klausmeier model of vegetation pattern formation. (English) Zbl 1403.35132 SIAM J. Appl. Math. 78, No. 6, 3213-3237 (2018). Reviewer: Andrey Zahariev (Plovdiv) MSC: 35K57 35C07 35B25 34C25 34C37 35B36 92D40 PDFBibTeX XMLCite \textit{P. Carter} and \textit{A. Doelman}, SIAM J. Appl. Math. 78, No. 6, 3213--3237 (2018; Zbl 1403.35132) Full Text: DOI
Thavanayagam, Ealasukanthan; Wall, David J. N. Modeling of spatial dynamical silence in the macro arterial domain. (English) Zbl 1408.37149 SIAM J. Appl. Dyn. Syst. 17, No. 3, 2176-2204 (2018). MSC: 37N25 37M05 74Q10 PDFBibTeX XMLCite \textit{E. Thavanayagam} and \textit{D. J. N. Wall}, SIAM J. Appl. Dyn. Syst. 17, No. 3, 2176--2204 (2018; Zbl 1408.37149) Full Text: DOI
Carter, Paul; Sandstede, Björn Unpeeling a homoclinic banana in the FitzHugh-Nagumo system. (English) Zbl 1407.35015 SIAM J. Appl. Dyn. Syst. 17, No. 1, 236-349 (2018). MSC: 35B25 35C07 34E15 34E17 35K57 PDFBibTeX XMLCite \textit{P. Carter} and \textit{B. Sandstede}, SIAM J. Appl. Dyn. Syst. 17, No. 1, 236--349 (2018; Zbl 1407.35015) Full Text: DOI
Li, Da-Peng Phase transition of oscillators and travelling waves in a class of relaxation systems. (English) Zbl 1392.34041 Discrete Contin. Dyn. Syst., Ser. B 21, No. 8, 2601-2614 (2016). Reviewer: Klaus R. Schneider (Berlin) MSC: 34C23 34C37 34C05 34E15 PDFBibTeX XMLCite \textit{D.-P. Li}, Discrete Contin. Dyn. Syst., Ser. B 21, No. 8, 2601--2614 (2016; Zbl 1392.34041) Full Text: DOI
Czechowski, Aleksander; Zgliczyński, Piotr Existence of periodic solutions of the Fitzhugh-Nagumo equations for an explicit range of the small parameter. (English) Zbl 1360.34069 SIAM J. Appl. Dyn. Syst. 15, No. 3, 1615-1655 (2016). Reviewer: Nikola Popovic (Edinburgh) MSC: 34C05 34C25 34E13 65G20 92C20 PDFBibTeX XMLCite \textit{A. Czechowski} and \textit{P. Zgliczyński}, SIAM J. Appl. Dyn. Syst. 15, No. 3, 1615--1655 (2016; Zbl 1360.34069) Full Text: DOI arXiv
Euzébio, Rodrigo D.; Llibre, Jaume; Vidal, Claudio Zero-Hopf bifurcation in the Fitzhugh-Nagumo system. (English) Zbl 1337.37036 Math. Methods Appl. Sci. 38, No. 17, 4289-4299 (2015). MSC: 37G15 37G10 34C07 35A24 PDFBibTeX XMLCite \textit{R. D. Euzébio} et al., Math. Methods Appl. Sci. 38, No. 17, 4289--4299 (2015; Zbl 1337.37036) Full Text: DOI arXiv Link
Carter, Paul; Sandstede, Björn Fast pulses with oscillatory tails in the FitzHugh-Nagumo system. (English) Zbl 1327.35008 SIAM J. Math. Anal. 47, No. 5, 3393-3441 (2015). MSC: 35B25 35C07 34E15 34C37 35B44 PDFBibTeX XMLCite \textit{P. Carter} and \textit{B. Sandstede}, SIAM J. Math. Anal. 47, No. 5, 3393--3441 (2015; Zbl 1327.35008) Full Text: DOI Link
Kristiansen, K. Uldall Computation of saddle-type slow manifolds using iterative methods. (English) Zbl 1323.34025 SIAM J. Appl. Dyn. Syst. 14, No. 2, 1189-1227 (2015). MSC: 34A45 34E15 34E13 37M99 34C45 34C37 92C20 PDFBibTeX XMLCite \textit{K. U. Kristiansen}, SIAM J. Appl. Dyn. Syst. 14, No. 2, 1189--1227 (2015; Zbl 1323.34025) Full Text: DOI arXiv
Arioli, Gianni; Koch, Hans Existence and stability of traveling pulse solutions of the FitzHugh-Nagumo equation. (English) Zbl 1304.35181 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 113, Part A, 51-70 (2015). MSC: 35C07 35K57 35B25 92C20 PDFBibTeX XMLCite \textit{G. Arioli} and \textit{H. Koch}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 113, 51--70 (2015; Zbl 1304.35181) Full Text: DOI
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