Raze, Ghislain; Volvert, Martin; Kerschen, Gaetan Tracking amplitude extrema of nonlinear frequency responses using the harmonic balance method. (English) Zbl 07801055 Int. J. Numer. Methods Eng. 125, No. 2, Article ID e7376, 28 p. (2024). MSC: 65D25 65L10 74H45 PDFBibTeX XMLCite \textit{G. Raze} et al., Int. J. Numer. Methods Eng. 125, No. 2, Article ID e7376, 28 p. (2024; Zbl 07801055) Full Text: DOI
Kogelbauer, Florian; Breunung, Thomas When does the method of harmonic balance give a correct prediction for mechanical systems? (English) Zbl 1517.37089 Appl. Anal. 102, No. 2, 425-443 (2023). MSC: 37M99 49M15 70K42 PDFBibTeX XMLCite \textit{F. Kogelbauer} and \textit{T. Breunung}, Appl. Anal. 102, No. 2, 425--443 (2023; Zbl 1517.37089) Full Text: DOI
Xing, Chengyue; Zhang, Zhengdi; Peng, Miao Bifurcation structures and bursting dynamics in a two degrees of freedom quasi-zero stiffness system with elastic constrain. (English) Zbl 1504.74037 Chaos Solitons Fractals 161, Article ID 112324, 12 p. (2022). MSC: 74H60 37G15 37G35 PDFBibTeX XMLCite \textit{C. Xing} et al., Chaos Solitons Fractals 161, Article ID 112324, 12 p. (2022; Zbl 1504.74037) Full Text: DOI
Ma, Wei; Mapuranga, Tafara; Zhang, Jiguang; Ding, Hejiang; Chen, Jiandong; Zhang, Xiao Bifurcation and path-following analysis of periodic orbits of a Fermi oscillator model. (English) Zbl 1507.37117 Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 12, Article ID 2250179, 26 p. (2022). MSC: 37M20 37G15 34C15 PDFBibTeX XMLCite \textit{W. Ma} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 12, Article ID 2250179, 26 p. (2022; Zbl 1507.37117) Full Text: DOI
Yan, Yao; Zhang, Baoquan; Páez Chávez, Joseph; Liu, Yang Optimising the locomotion of a vibro-impact capsule robot self-propelling in the small intestine. (English) Zbl 1502.37097 Commun. Nonlinear Sci. Numer. Simul. 114, Article ID 106696, 17 p. (2022). MSC: 37N25 92C32 92C50 PDFBibTeX XMLCite \textit{Y. Yan} et al., Commun. Nonlinear Sci. Numer. Simul. 114, Article ID 106696, 17 p. (2022; Zbl 1502.37097) Full Text: DOI
Erhardt, André H.; Solem, Susanne Bifurcation analysis of a modified cardiac cell model. (English) Zbl 1489.37106 SIAM J. Appl. Dyn. Syst. 21, No. 1, 231-247 (2022). MSC: 37N25 92B05 92C30 PDFBibTeX XMLCite \textit{A. H. Erhardt} and \textit{S. Solem}, SIAM J. Appl. Dyn. Syst. 21, No. 1, 231--247 (2022; Zbl 1489.37106) Full Text: DOI
Qin, B. W.; Chung, K. W.; Algaba, A.; Rodríguez-Luis, A. J. High-order approximation of heteroclinic bifurcations in truncated 2D-normal forms for the generic cases of Hopf-zero and nonresonant double Hopf singularities. (English) Zbl 1478.34067 SIAM J. Appl. Dyn. Syst. 20, No. 1, 403-437 (2021). Reviewer: Tao Li (Chengdu) MSC: 34E05 34E10 34C37 37M20 41A60 34C20 34C23 PDFBibTeX XMLCite \textit{B. W. Qin} et al., SIAM J. Appl. Dyn. Syst. 20, No. 1, 403--437 (2021; Zbl 1478.34067) Full Text: DOI
Erhardt, André H.; Solem, Susanne On complex dynamics in a Purkinje and a ventricular cardiac cell model. (English) Zbl 1454.37089 Commun. Nonlinear Sci. Numer. Simul. 93, Article ID 105511, 21 p. (2021). MSC: 37N25 37G15 35Q92 65P30 92B05 PDFBibTeX XMLCite \textit{A. H. Erhardt} and \textit{S. Solem}, Commun. Nonlinear Sci. Numer. Simul. 93, Article ID 105511, 21 p. (2021; Zbl 1454.37089) Full Text: DOI arXiv
Hafez, Omar A.; Gottschalk, Allan Altered neuronal excitability in a Hodgkin-Huxley model incorporating channelopathies of the delayed rectifier Potassium channel. (English) Zbl 1489.92038 J. Comput. Neurosci. 48, No. 4, 377-386 (2020). MSC: 92C32 92C20 PDFBibTeX XMLCite \textit{O. A. Hafez} and \textit{A. Gottschalk}, J. Comput. Neurosci. 48, No. 4, 377--386 (2020; Zbl 1489.92038) Full Text: DOI
Páez Chávez, Joseph; Zhang, Zhi; Liu, Yang A numerical approach for the bifurcation analysis of nonsmooth delay equations. (English) Zbl 1451.65080 Commun. Nonlinear Sci. Numer. Simul. 83, Article ID 105095, 16 p. (2020). MSC: 65L03 37M20 34A36 34K18 PDFBibTeX XMLCite \textit{J. Páez Chávez} et al., Commun. Nonlinear Sci. Numer. Simul. 83, Article ID 105095, 16 p. (2020; Zbl 1451.65080) Full Text: DOI
Wei, Junqiang Numerical optimization method for determination of bifurcation points and its application in stability analysis of power system. (English) Zbl 07124750 Int. J. Comput. Methods 17, No. 2, Article ID 1850126, 13 p. (2020). MSC: 65-XX 37-XX PDFBibTeX XMLCite \textit{J. Wei}, Int. J. Comput. Methods 17, No. 2, Article ID 1850126, 13 p. (2020; Zbl 07124750) Full Text: DOI
Wouters, Michiel; Vanroose, Wim Automatic exploration techniques of numerical bifurcation diagrams illustrated by the Ginzburg-Landau equation. (English) Zbl 1431.37066 SIAM J. Appl. Dyn. Syst. 18, No. 4, 2047-2098 (2019). MSC: 37M20 35Q56 PDFBibTeX XMLCite \textit{M. Wouters} and \textit{W. Vanroose}, SIAM J. Appl. Dyn. Syst. 18, No. 4, 2047--2098 (2019; Zbl 1431.37066) Full Text: DOI arXiv
Van Kekem, Dirk L.; Sterk, Alef E. Symmetries in the Lorenz-96 model. (English) Zbl 1415.34040 Int. J. Bifurcation Chaos Appl. Sci. Eng. 29, No. 1, Article ID 1950008, 18 p. (2019). MSC: 34A34 34C14 34C23 34C45 37G40 34C05 PDFBibTeX XMLCite \textit{D. L. Van Kekem} and \textit{A. E. Sterk}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 29, No. 1, Article ID 1950008, 18 p. (2019; Zbl 1415.34040) Full Text: DOI arXiv
Spiliotis, Konstantinos; Russo, Lucia; Giannino, Francesco; Cuomo, Salvatore; Siettos, Constantinos; Toraldo, Gerardo Nonlinear Galerkin methods for a system of PDEs with Turing instabilities. (English) Zbl 1448.65247 Calcolo 55, No. 1, Paper No. 9, 23 p. (2018). MSC: 65N30 65M06 65L05 37L65 35B40 35B36 35B38 35B32 92C80 92C15 PDFBibTeX XMLCite \textit{K. Spiliotis} et al., Calcolo 55, No. 1, Paper No. 9, 23 p. (2018; Zbl 1448.65247) Full Text: DOI
Banerjee, M.; Kooi, Bob W.; Venturino, E. An ecoepidemic model with prey herd behavior and predator feeding saturation response on both healthy and diseased prey. (English) Zbl 1384.37112 Math. Model. Nat. Phenom. 12, No. 2, 133-161 (2017). MSC: 37N25 37G35 92D30 92D25 92D40 PDFBibTeX XMLCite \textit{M. Banerjee} et al., Math. Model. Nat. Phenom. 12, No. 2, 133--161 (2017; Zbl 1384.37112) Full Text: DOI Link
Pandey, Vikas; Singh, Suneet A bifurcation analysis of boiling water reactor on large domain of parametric spaces. (English) Zbl 1471.82035 Commun. Nonlinear Sci. Numer. Simul. 38, 30-44 (2016). MSC: 82D75 37N20 PDFBibTeX XMLCite \textit{V. Pandey} and \textit{S. Singh}, Commun. Nonlinear Sci. Numer. Simul. 38, 30--44 (2016; Zbl 1471.82035) Full Text: DOI
Kutafina, Ekaterina Mixed mode oscillations in the Bonhoeffer-van der Pol oscillator with weak periodic perturbation. (English) Zbl 1319.34072 Comput. Appl. Math. 34, No. 1, 81-92 (2015). MSC: 34C26 34E13 34E17 37C60 34C15 34E15 92C20 PDFBibTeX XMLCite \textit{E. Kutafina}, Comput. Appl. Math. 34, No. 1, 81--92 (2015; Zbl 1319.34072) Full Text: DOI arXiv
Govaerts, Willy; Sonck, Charlotte Computational study of a budding yeast model of Tyson and Novák. (English) Zbl 1519.92065 Math. Comput. Simul. 96, 207-223 (2014). MSC: 92C37 92C70 34C23 PDFBibTeX XMLCite \textit{W. Govaerts} and \textit{C. Sonck}, Math. Comput. Simul. 96, 207--223 (2014; Zbl 1519.92065) Full Text: DOI
Bulelzai, M. A. K.; Dubbeldam, J. L. A.; Meijer, H. G. E. Bifurcation analysis of a model for atherosclerotic plaque evolution. (English) Zbl 1349.92072 Physica D 278-279, 31-43 (2014). MSC: 92C50 37N25 37G10 37M05 PDFBibTeX XMLCite \textit{M. A. K. Bulelzai} et al., Physica D 278--279, 31--43 (2014; Zbl 1349.92072) Full Text: DOI Link
Petit, F.; Loccufier, M.; Aeyels, D. The energy thresholds of nonlinear vibration absorbers. (English) Zbl 1279.74017 Nonlinear Dyn. 74, No. 3, 755-767 (2013). MSC: 74H45 34A35 37G15 34C15 PDFBibTeX XMLCite \textit{F. Petit} et al., Nonlinear Dyn. 74, No. 3, 755--767 (2013; Zbl 1279.74017) Full Text: DOI
Kuehn, Christian A mathematical framework for critical transitions: normal forms, variance and applications. (English) Zbl 1282.34062 J. Nonlinear Sci. 23, No. 3, 457-510 (2013). Reviewer: Romeo Negrea (Timisoara) MSC: 34F05 34E15 60H10 34C23 37M10 34C20 PDFBibTeX XMLCite \textit{C. Kuehn}, J. Nonlinear Sci. 23, No. 3, 457--510 (2013; Zbl 1282.34062) Full Text: DOI arXiv
Desroches, Mathieu; Guckenheimer, John; Krauskopf, Bernd; Kuehn, Christian; Osinga, Hinke M.; Wechselberger, Martin Mixed-mode oscillations with multiple time scales. (English) Zbl 1250.34001 SIAM Rev. 54, No. 2, 211-288 (2012). MSC: 34-02 34C23 34E13 34E15 34E17 34C37 34C45 65L11 PDFBibTeX XMLCite \textit{M. Desroches} et al., SIAM Rev. 54, No. 2, 211--288 (2012; Zbl 1250.34001) Full Text: DOI
Guckenheimer, John; Osinga, Hinke M. The singular limit of a Hopf bifurcation. (English) Zbl 1402.37060 Discrete Contin. Dyn. Syst. 32, No. 8, 2805-2823 (2012). MSC: 37G10 34C23 34E13 34C20 34D15 PDFBibTeX XMLCite \textit{J. Guckenheimer} and \textit{H. M. Osinga}, Discrete Contin. Dyn. Syst. 32, No. 8, 2805--2823 (2012; Zbl 1402.37060) Full Text: DOI
Wei, Jun-Qiang; Yang, Zhong-Hua A novel method for computation of higher order singular points in nonlinear problems with single parameter. (English) Zbl 1251.65077 J. Comput. Appl. Math. 236, No. 6, 1442-1448 (2011). Reviewer: Yanlai Chen (North Dartmouth) MSC: 65H20 34B15 37M20 65P30 PDFBibTeX XMLCite \textit{J.-Q. Wei} and \textit{Z.-H. Yang}, J. Comput. Appl. Math. 236, No. 6, 1442--1448 (2011; Zbl 1251.65077) Full Text: DOI
Hughes, J.; Friedman, M. A bisection-like algorithm for branch switching at a simple branch point. (English) Zbl 1203.37006 J. Sci. Comput. 41, No. 1, 62-69 (2009). MSC: 37-04 37M20 65P30 PDFBibTeX XMLCite \textit{J. Hughes} and \textit{M. Friedman}, J. Sci. Comput. 41, No. 1, 62--69 (2009; Zbl 1203.37006) Full Text: DOI
Dhooge, A.; Govaerts, W.; Kuznetsov, Yu. A.; Meijer, H. G. E.; Sautois, B. New features of the software MatCont for bifurcation analysis of dynamical systems. (English) Zbl 1158.34302 Math. Comput. Model. Dyn. Syst. 14, No. 2, 147-175 (2008). MSC: 34-04 34C23 34C20 37M20 65P30 PDFBibTeX XMLCite \textit{A. Dhooge} et al., Math. Comput. Model. Dyn. Syst. 14, No. 2, 147--175 (2008; Zbl 1158.34302) Full Text: DOI
di Bernardo, M.; Budd, C. J.; Champneys, A. R.; Kowalczyk, P. Piecewise-smooth dynamical systems. Theory and applications. (English) Zbl 1146.37003 Applied Mathematical Sciences 163. New York, NY: Springer (ISBN 978-1-84628-039-9/hbk). xxi, 481 p. (2008). Reviewer: Jan Sieber (Portsmouth) MSC: 37-01 34A36 37G10 37G15 37N05 70G40 37N20 37C10 37C27 37D45 PDFBibTeX XMLCite \textit{M. di Bernardo} et al., Piecewise-smooth dynamical systems. Theory and applications. New York, NY: Springer (2008; Zbl 1146.37003)
Janovská, Dáša; Janovský, Vladimír A postprocessing of Hopf bifurcation points. (English) Zbl 1056.65140 Feistauer, M. (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2003, the 5th European conference on numerical mathematics and advanced applications, Prague, Czech Republic, August 18–22, 2003. Berlin: Springer (ISBN 3-540-21460-7/hbk). 502-509 (2004). MSC: 65P30 37C27 37G15 37M20 PDFBibTeX XMLCite \textit{D. Janovská} and \textit{V. Janovský}, in: Numerical mathematics and advanced applications. Proceedings of ENUMATH 2003, the 5th European conference on numerical mathematics and advanced applications, Prague, Czech Republic, August 18--22, 2003. Berlin: Springer. 502--509 (2004; Zbl 1056.65140)