Hammerlindl, Andy; Krauskopf, Bernd; Mason, Gemma; Osinga, Hinke M. Determining the global manifold structure of a continuous-time heterodimensional cycle. (English) Zbl 1503.34079 J. Comput. Dyn. 9, No. 3, 393-419 (2022). MSC: 34C05 34C37 34C45 37M21 92C37 PDFBibTeX XMLCite \textit{A. Hammerlindl} et al., J. Comput. Dyn. 9, No. 3, 393--419 (2022; Zbl 1503.34079) Full Text: DOI arXiv
Hasan, Cris R.; Osinga, Hinke M.; Postlethwaite, Claire M.; Rucklidge, Alastair M. Spatiotemporal stability of periodic travelling waves in a heteroclinic-cycle model. (English) Zbl 1475.37085 Nonlinearity 34, No. 8, 5576-5598 (2021). Reviewer: Alain Brillard (Riedisheim) MSC: 37L15 35C07 35B06 35B35 37M20 35Q91 PDFBibTeX XMLCite \textit{C. R. Hasan} et al., Nonlinearity 34, No. 8, 5576--5598 (2021; Zbl 1475.37085) Full Text: DOI arXiv
Musoke, Elle; Krauskopf, Bernd; Osinga, Hinke M. A surface of heteroclinic connections between two saddle slow manifolds in the Olsen model. (English) Zbl 1461.34072 Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 16, Article ID 2030048, 33 p. (2020). MSC: 34C60 34C45 92C45 34E20 34C05 34C37 37M21 PDFBibTeX XMLCite \textit{E. Musoke} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 16, Article ID 2030048, 33 p. (2020; Zbl 1461.34072) Full Text: DOI
Hittmeyer, Stefanie; Krauskopf, Bernd; Osinga, Hinke M.; Shinohara, Katsutoshi How to identify a hyperbolic set as a blender. (English) Zbl 1457.37044 Discrete Contin. Dyn. Syst. 40, No. 12, 6815-6836 (2020). Reviewer: Matheus Cheque Bortolan (Florianópolis) MSC: 37D05 37D25 37D10 37C05 37G25 37M21 PDFBibTeX XMLCite \textit{S. Hittmeyer} et al., Discrete Contin. Dyn. Syst. 40, No. 12, 6815--6836 (2020; Zbl 1457.37044) Full Text: DOI
Langfield, Peter; Krauskopf, Bernd; Osinga, Hinke M. A continuation approach to computing phase resetting curves. (English) Zbl 1454.37082 Junge, Oliver (ed.) et al., Advances in dynamics, optimization and computation. A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday. Cham: Springer. Stud. Syst. Decis. Control 304, 3-30 (2020). MSC: 37M21 37M05 PDFBibTeX XMLCite \textit{P. Langfield} et al., Stud. Syst. Decis. Control 304, 3--30 (2020; Zbl 1454.37082) Full Text: DOI arXiv
Giraldo, Andrus; Krauskopf, Bernd; Osinga, Hinke M. Computing connecting orbits to infinity associated with a homoclinic flip bifurcation. (English) Zbl 1450.37074 J. Comput. Dyn. 7, No. 2, 489-510 (2020). MSC: 37M20 37M21 37C29 37G25 PDFBibTeX XMLCite \textit{A. Giraldo} et al., J. Comput. Dyn. 7, No. 2, 489--510 (2020; Zbl 1450.37074) Full Text: DOI
Hittmeyer, Stefanie; Krauskopf, Bernd; Osinga, Hinke M. Generalized Mandelbrot and Julia sets in a family of planar angle-doubling maps. (English) Zbl 1453.37040 Bohner, Martin (ed.) et al., Difference equations and discrete dynamical systems with applications. ICDEA 24, Dresden, Germany, May 21–25, 2018. Proceedings of the 24th international conference on difference equations and applications. Cham: Springer. Springer Proc. Math. Stat. 312, 21-54 (2020). Reviewer: Tao Chen (New York) MSC: 37F10 37F12 30D05 65E05 65E10 PDFBibTeX XMLCite \textit{S. Hittmeyer} et al., Springer Proc. Math. Stat. 312, 21--54 (2020; Zbl 1453.37040) Full Text: DOI
Giraldo, Andrus; Krauskopf, Bernd; Osinga, Hinke M. Cascades of global bifurcations and chaos near a homoclinic flip bifurcation: a case study. (English) Zbl 1408.37087 SIAM J. Appl. Dyn. Syst. 17, No. 4, 2784-2829 (2018). MSC: 37G20 37C29 37M20 34C45 34C23 37D45 PDFBibTeX XMLCite \textit{A. Giraldo} et al., SIAM J. Appl. Dyn. Syst. 17, No. 4, 2784--2829 (2018; Zbl 1408.37087) Full Text: DOI
Hittmeyer, Stefanie; Krauskopf, Bernd; Osinga, Hinke M.; Shinohara, Katsutoshi Existence of blenders in a Hénon-like family: geometric insights from invariant manifold computations. (English) Zbl 1402.37027 Nonlinearity 31, No. 10, R239-R267 (2018). Reviewer: Irina V. Konopleva (Ul’yanovsk) MSC: 37C05 37D25 37D10 37M20 PDFBibTeX XMLCite \textit{S. Hittmeyer} et al., Nonlinearity 31, No. 10, R239--R267 (2018; Zbl 1402.37027) Full Text: DOI
Hasan, Cris R.; Krauskopf, Bernd; Osinga, Hinke M. Saddle slow manifolds and canard orbits in \(\mathbb{R}^{4}\) and application to the full Hodgkin-Huxley model. (English) Zbl 1395.92038 J. Math. Neurosci. 8, Paper No. 5, 48 p. (2018). MSC: 92C20 37N25 34E17 34E15 PDFBibTeX XMLCite \textit{C. R. Hasan} et al., J. Math. Neurosci. 8, Paper No. 5, 48 p. (2018; Zbl 1395.92038) Full Text: DOI
Farjami, Saeed; Kirk, Vivien; Osinga, Hinke M. Computing the stable manifold of a saddle slow manifold. (English) Zbl 1403.37036 SIAM J. Appl. Dyn. Syst. 17, No. 1, 350-379 (2018). Reviewer: Josef Diblík (Brno) MSC: 37D10 37M20 34D15 34E15 37C10 65L10 34D35 34C45 65P40 70K70 PDFBibTeX XMLCite \textit{S. Farjami} et al., SIAM J. Appl. Dyn. Syst. 17, No. 1, 350--379 (2018; Zbl 1403.37036) Full Text: DOI
Mujica, José; Krauskopf, Bernd; Osinga, Hinke M. A Lin’s method approach for detecting all canard orbits arising from a folded node. (English) Zbl 1397.34096 J. Comput. Dyn. 4, No. 1-2, 143-165 (2017). MSC: 34E17 65L10 34B15 65L11 34A45 34E15 34C45 37M99 PDFBibTeX XMLCite \textit{J. Mujica} et al., J. Comput. Dyn. 4, No. 1--2, 143--165 (2017; Zbl 1397.34096) Full Text: DOI
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
Creaser, Jennifer L.; Krauskopf, Bernd; Osinga, Hinke M. Finding first foliation tangencies in the Lorenz system. (English) Zbl 1381.37097 SIAM J. Appl. Dyn. Syst. 16, No. 4, 2127-2164 (2017). MSC: 37M20 37D10 37D45 37C29 65L10 65P30 PDFBibTeX XMLCite \textit{J. L. Creaser} et al., SIAM J. Appl. Dyn. Syst. 16, No. 4, 2127--2164 (2017; Zbl 1381.37097) Full Text: DOI
Giraldo, Andrus; Krauskopf, Bernd; Osinga, Hinke M. Saddle invariant objects and their global manifolds in a neighborhood of a homoclinic flip bifurcation of case B. (English) Zbl 1385.37028 SIAM J. Appl. Dyn. Syst. 16, No. 1, 640-686 (2017). Reviewer: Kwok-wai Chung (Hong Kong) MSC: 37C29 37M20 37G25 34C23 37D45 37C15 37D10 37G20 PDFBibTeX XMLCite \textit{A. Giraldo} et al., SIAM J. Appl. Dyn. Syst. 16, No. 1, 640--686 (2017; Zbl 1385.37028) Full Text: DOI
Krauskopf, Bernd; Osinga, Hinke M. A codimension-four singularity with potential for action. (English) Zbl 1365.34071 Toni, Bourama (ed.), Mathematical sciences with multidisciplinary applications. In honor of Professor Christiane Rousseau, and in recognition of the Mathematics for Planet Earth initiative. Cham: Springer (ISBN 978-3-319-31321-4/hbk; 978-3-319-31323-8/ebook). Springer Proceedings in Mathematics & Statistics 157, 253-268 (2016). MSC: 34C23 34C37 PDFBibTeX XMLCite \textit{B. Krauskopf} and \textit{H. M. Osinga}, Springer Proc. Math. Stat. 157, 253--268 (2016; Zbl 1365.34071) Full Text: DOI
Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M.; Sandstede, Björn Invariant manifolds and global bifurcations. (English) Zbl 1374.37076 Chaos 25, No. 9, 097604, 13 p. (2015). MSC: 37J15 37D10 37G99 PDFBibTeX XMLCite \textit{J. Guckenheimer} et al., Chaos 25, No. 9, 097604, 13 p. (2015; Zbl 1374.37076) Full Text: DOI Link
Hittmeyer, Stefanie; Krauskopf, Bernd; Osinga, Hinke M. From wild Lorenz-like to wild Rovella-like dynamics. (English) Zbl 1357.37059 Dyn. Syst. 30, No. 4, 525-542 (2015). MSC: 37D45 37G20 37G25 37G35 65P30 PDFBibTeX XMLCite \textit{S. Hittmeyer} et al., Dyn. Syst. 30, No. 4, 525--542 (2015; Zbl 1357.37059) Full Text: DOI
Doedel, Eusebius J.; Krauskopf, Bernd; Osinga, Hinke M. Global organization of phase space in the transition to chaos in the Lorenz system. (English) Zbl 1332.34083 Nonlinearity 28, No. 11, R113-R139 (2015). MSC: 34C45 34C37 34A34 34C28 34D45 34C23 65P99 PDFBibTeX XMLCite \textit{E. J. Doedel} et al., Nonlinearity 28, No. 11, R113--R139 (2015; Zbl 1332.34083) Full Text: DOI
Langfield, Peter; Krauskopf, Bernd; Osinga, Hinke M. Forward-time and backward-time isochrons and their interactions. (English) Zbl 1358.37047 SIAM J. Appl. Dyn. Syst. 14, No. 3, 1418-1453 (2015). MSC: 37C10 37C27 37D10 37G25 92B25 PDFBibTeX XMLCite \textit{P. Langfield} et al., SIAM J. Appl. Dyn. Syst. 14, No. 3, 1418--1453 (2015; Zbl 1358.37047) Full Text: DOI
Hittmeyer, Stefanie; Krauskopf, Bernd; Osinga, Hinke M. Interactions of the Julia set with critical and (un)stable sets in an angle-doubling map on \(\mathbb{C}\backslash\{0\}\). (English) Zbl 1314.37034 Int. J. Bifurcation Chaos Appl. Sci. Eng. 25, No. 4, Article ID 1530013, 36 p. (2015). MSC: 37F50 37M25 37G25 37F45 PDFBibTeX XMLCite \textit{S. Hittmeyer} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 25, No. 4, Article ID 1530013, 36 p. (2015; Zbl 1314.37034) Full Text: DOI
Langfield, Peter; Krauskopf, Bernd; Osinga, Hinke M. Solving Winfree’s puzzle: the isochrons in the FitzHugh-Nagumo model. (English) Zbl 1374.37032 Chaos 24, No. 1, 013131, 13 p. (2014). MSC: 37C10 37N25 92B05 37D10 37D05 PDFBibTeX XMLCite \textit{P. Langfield} et al., Chaos 24, No. 1, 013131, 13 p. (2014; Zbl 1374.37032) Full Text: DOI Link
Osinga, Hinke M.; Krauskopf, Bernd; Hittmeyer, Stefanie Chaos and wild chaos in Lorenz-type systems. (English) Zbl 1318.37009 AlSharawi, Ziyad (ed.) et al., Theory and applications of difference equations and discrete dynamical systems. ICDEA, Muscat, Oman, May 26–30, 2013. Berlin: Springer (ISBN 978-3-662-44139-8/hbk; 978-3-662-44140-4/ebook). Springer Proceedings in Mathematics & Statistics 102, 75-98 (2014). MSC: 37D45 37-02 70K55 PDFBibTeX XMLCite \textit{H. M. Osinga} et al., Springer Proc. Math. Stat. 102, 75--98 (2014; Zbl 1318.37009) Full Text: DOI
Aguirre, Pablo; Krauskopf, Bernd; Osinga, Hinke M. Global invariant manifolds near a Shilnikov homoclinic bifurcation. (English) Zbl 1309.34077 J. Comput. Dyn. 1, No. 1, 1-38 (2014). MSC: 34C37 34C45 37D45 34C23 37M99 PDFBibTeX XMLCite \textit{P. Aguirre} et al., J. Comput. Dyn. 1, No. 1, 1--38 (2014; Zbl 1309.34077) Full Text: DOI
Doedel, Eusebius J.; Krauskopf, Bernd; Osinga, Hinke M. Global invariant manifolds in the transition to preturbulence in the Lorenz system. (English) Zbl 1246.37037 Indag. Math., New Ser. 22, No. 3-4, 222-240 (2011). Reviewer: Kwok-wai Chung (Hong Kong) MSC: 37C10 37C29 37D10 37G15 PDFBibTeX XMLCite \textit{E. J. Doedel} et al., Indag. Math., New Ser. 22, No. 3--4, 222--240 (2011; Zbl 1246.37037) Full Text: DOI
Nowacki, Jakub; Mazlan, Siti; Osinga, Hinke M.; Tsaneva-Atanasova, Krasimira The role of large-conductance calcium-activated K\(^+\) (BK) channels in shaping bursting oscillations of a somatotroph cell model. (English) Zbl 1186.92014 Physica D 239, No. 9, 485-493 (2010). MSC: 92C37 92C05 92C30 PDFBibTeX XMLCite \textit{J. Nowacki} et al., Physica D 239, No. 9, 485--493 (2010; Zbl 1186.92014) Full Text: DOI
Hobbs, C. A.; Osinga, H. M. Bifurcations of the global stable set of a planar endomorphism near a cusp singularity. (English) Zbl 1165.37307 Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 8, 2207-2222 (2008). MSC: 37C05 37G05 37G10 37D10 PDFBibTeX XMLCite \textit{C. A. Hobbs} and \textit{H. M. Osinga}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 8, 2207--2222 (2008; Zbl 1165.37307) Full Text: DOI
Krauskopf, Bernd; Osinga, Hinke M.; Doedel, Eusebius J. Visualizing global manifolds during the transition to chaos in the Lorenz system. (English) Zbl 1185.37079 Hege, Hans-Christian (ed.) et al., Topology-based methods in visualization II. Papers based on the 2nd workshop on topological methods in visualization, Kloster Nimbschen near Leipzig, Germany, March 4–6, 2007. Berlin: Springer (ISBN 978-3-540-88605-1/hbk). Mathematics and Visualization, 115-126 (2008). Reviewer: Gasanbek T. Arazov (Baku) MSC: 37D45 PDFBibTeX XMLCite \textit{B. Krauskopf} et al., in: Topology-based methods in visualization II. Papers based on the 2nd workshop on topological methods in visualization, Kloster Nimbschen near Leipzig, Germany, March 4--6, 2007. Berlin: Springer. 115--126 (2008; Zbl 1185.37079) Full Text: DOI Link
Osinga, H. M.; Krauskopf, B. Visualizing curvature on the Lorenz manifold. (English) Zbl 1122.53001 J. Math. Arts 1, No. 2, 113-123 (2007). MSC: 53A05 53A45 37M20 65P40 65D18 PDFBibTeX XMLCite \textit{H. M. Osinga} and \textit{B. Krauskopf}, J. Math. Arts 1, No. 2, 113--123 (2007; Zbl 1122.53001) Full Text: DOI Link
Krauskopf, B.; Osinga, H. M.; Doedel, E. J.; Henderson, M. E.; Guckenheimer, J.; Vladimirsky, A.; Dellnitz, M.; Junge, O. A survey of methods for computing (un)stable manifolds of vector fields. (English) Zbl 1086.34002 Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, No. 3, 763-791 (2005). Reviewer: Sergiy Yanchuk (Berlin) MSC: 34-02 34C30 65L99 34C28 37C10 PDFBibTeX XMLCite \textit{B. Krauskopf} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, No. 3, 763--791 (2005; Zbl 1086.34002) Full Text: DOI
Osinga, H. M.; Rokni Lamooki, G. R.; Townley, S. Numerical approximations of strong (un)stable manifolds. (English) Zbl 1058.37062 Dyn. Syst. 19, No. 3, 195-215 (2004). MSC: 37M20 37D10 65P40 37C10 PDFBibTeX XMLCite \textit{H. M. Osinga} et al., Dyn. Syst. 19, No. 3, 195--215 (2004; Zbl 1058.37062) Full Text: DOI
Krauskopf, Bernd; Osinga, Hinke Globalizing two-dimensional unstable manifolds of maps. (English) Zbl 0955.37016 Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, No. 3, 483-503 (1998). Reviewer: Alois Klíč (Praha) MSC: 37D10 37C50 37M99 PDFBibTeX XMLCite \textit{B. Krauskopf} and \textit{H. Osinga}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, No. 3, 483--503 (1998; Zbl 0955.37016) Full Text: DOI