Kristiansen, K. Uldall The dud canard: existence of strong canard cycles in \(\mathbb{R}^3\). (English) Zbl 07748212 J. Differ. Equations 375, 706-749 (2023). Reviewer: Jianhe Shen (Fuzhou) MSC: 34E17 34E15 34C23 34C05 34C45 PDFBibTeX XMLCite \textit{K. U. Kristiansen}, J. Differ. Equations 375, 706--749 (2023; Zbl 07748212) Full Text: DOI arXiv
Li, Chengzhi; Liu, Changjian A proof of a Dumortier-Roussarie’s conjecture. (English) Zbl 1512.34074 Discrete Contin. Dyn. Syst., Ser. S 16, No. 3-4, 460-473 (2023). MSC: 34C07 34C08 37G15 PDFBibTeX XMLCite \textit{C. Li} and \textit{C. Liu}, Discrete Contin. Dyn. Syst., Ser. S 16, No. 3--4, 460--473 (2023; Zbl 1512.34074) Full Text: DOI
De Maesschalck, Peter; Huzak, Renato; Janssens, Ansfried; Radunović, Goran Fractal codimension of nilpotent contact points in two-dimensional slow-fast systems. (English) Zbl 1516.34087 J. Differ. Equations 355, 162-192 (2023). MSC: 34E15 34E17 34C40 28A80 28A75 34C23 34C05 PDFBibTeX XMLCite \textit{P. De Maesschalck} et al., J. Differ. Equations 355, 162--192 (2023; Zbl 1516.34087) Full Text: DOI arXiv
Huzak, Renato; Vlah, Domagoj; Žubrinić, Darko; Županović, Vesna Fractal analysis of degenerate spiral trajectories of a class of ordinary differential equations. (English) Zbl 1510.37043 Appl. Math. Comput. 438, Article ID 127569, 15 p. (2023). MSC: 37C45 34C28 PDFBibTeX XMLCite \textit{R. Huzak} et al., Appl. Math. Comput. 438, Article ID 127569, 15 p. (2023; Zbl 1510.37043) Full Text: DOI arXiv
Huzak, Renato; Rojas, David Abelian integrals and non-generic turning points. (English) Zbl 1504.34084 Qual. Theory Dyn. Syst. 21, No. 3, Paper No. 77, 18 p. (2022). Reviewer: Xiuli Cen (Zhuhai) MSC: 34C08 34E15 34E17 PDFBibTeX XMLCite \textit{R. Huzak} and \textit{D. Rojas}, Qual. Theory Dyn. Syst. 21, No. 3, Paper No. 77, 18 p. (2022; Zbl 1504.34084) Full Text: DOI
Liu, Changjian; Li, Chengzhi; Llibre, Jaume The cyclicity of the period annulus of a reversible quadratic system. (English) Zbl 1508.34030 Proc. R. Soc. Edinb., Sect. A, Math. 152, No. 2, 281-290 (2022). Reviewer: Jeidy Johana Jimenez (Goiânia) MSC: 34C07 34C08 34C23 34E10 34C14 34C05 PDFBibTeX XMLCite \textit{C. Liu} et al., Proc. R. Soc. Edinb., Sect. A, Math. 152, No. 2, 281--290 (2022; Zbl 1508.34030) Full Text: DOI Link
Huzak, Renato Cyclicity of canard cycles with hyperbolic saddles located away from the critical curve. (English) Zbl 1493.34163 J. Differ. Equations 320, 479-509 (2022). MSC: 34E17 34C07 34C23 34C05 34E15 34C26 34E20 PDFBibTeX XMLCite \textit{R. Huzak}, J. Differ. Equations 320, 479--509 (2022; Zbl 1493.34163) 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
De Maesschalck, Peter; Doan, Thai Son; Wynen, Jeroen Intrinsic determination of the criticality of a slow-fast Hopf bifurcation. (English) Zbl 1491.34069 J. Dyn. Differ. Equations 33, No. 4, 2253-2269 (2021). Reviewer: Nikola Popovic (Edinburgh) MSC: 34E15 34C23 34C20 37G10 34C05 34D20 PDFBibTeX XMLCite \textit{P. De Maesschalck} et al., J. Dyn. Differ. Equations 33, No. 4, 2253--2269 (2021; Zbl 1491.34069) 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
Huzak, Renato; Crnković, Vlatko; Vlah, Domagoj Fractal dimensions and two-dimensional slow-fast systems. (English) Zbl 1470.34150 J. Math. Anal. Appl. 501, No. 2, Article ID 125212, 21 p. (2021). MSC: 34E15 34A26 34E17 34C23 11M41 28A80 37C45 PDFBibTeX XMLCite \textit{R. Huzak} et al., J. Math. Anal. Appl. 501, No. 2, Article ID 125212, 21 p. (2021; Zbl 1470.34150) Full Text: DOI
Cen, Xiuli; Liu, Changjian; Zhao, Yulin New family of abelian integrals satisfying Chebyshev property. (English) Zbl 1464.34056 J. Differ. Equations 268, No. 12, 7561-7581 (2020). Reviewer: Maite Grau (Lleida) MSC: 34C08 34C07 37G15 PDFBibTeX XMLCite \textit{X. Cen} et al., J. Differ. Equations 268, No. 12, 7561--7581 (2020; Zbl 1464.34056) Full Text: DOI
Wang, Cheng; Zhang, Xiang Canards, heteroclinic and homoclinic orbits for a slow-fast predator-prey model of generalized Holling type III. (English) Zbl 1418.34103 J. Differ. Equations 267, No. 6, 3397-3441 (2019). MSC: 34C60 34C37 34C26 92D25 34E15 34E17 PDFBibTeX XMLCite \textit{C. Wang} and \textit{X. Zhang}, J. Differ. Equations 267, No. 6, 3397--3441 (2019; Zbl 1418.34103) Full Text: DOI
Huzak, Renato Canard explosion near non-Liénard type slow-fast Hopf point. (English) Zbl 1426.34071 J. Dyn. Differ. Equations 31, No. 2, 683-709 (2019). Reviewer: Robert Vrabel (Trnava) MSC: 34E17 34C23 34E15 34C05 34E10 PDFBibTeX XMLCite \textit{R. Huzak}, J. Dyn. Differ. Equations 31, No. 2, 683--709 (2019; Zbl 1426.34071) Full Text: DOI
Huzak, Renato Box dimension and cyclicity of Canard cycles. (English) Zbl 1402.34063 Qual. Theory Dyn. Syst. 17, No. 2, 475-493 (2018). MSC: 34E17 34C07 34C26 37C45 34E15 PDFBibTeX XMLCite \textit{R. Huzak}, Qual. Theory Dyn. Syst. 17, No. 2, 475--493 (2018; Zbl 1402.34063) Full Text: DOI Link
Marín, D.; Villadelprat, J. On the Chebyshev property of certain abelian integrals near a polycycle. (English) Zbl 1394.34058 Qual. Theory Dyn. Syst. 17, No. 1, 261-270 (2018). Reviewer: Valery A. Gaiko (Minsk) MSC: 34C08 34C37 34E15 PDFBibTeX XMLCite \textit{D. Marín} and \textit{J. Villadelprat}, Qual. Theory Dyn. Syst. 17, No. 1, 261--270 (2018; Zbl 1394.34058) Full Text: DOI Link
Huzak, Renato Normal forms of Liénard type for analytic unfoldings of nilpotent singularities. (English) Zbl 1378.37086 Proc. Am. Math. Soc. 145, No. 10, 4325-4336 (2017). Reviewer: Mohamed Selmi (Sousse-Riadh) MSC: 37G05 34M45 32G05 58H10 58H15 PDFBibTeX XMLCite \textit{R. Huzak}, Proc. Am. Math. Soc. 145, No. 10, 4325--4336 (2017; Zbl 1378.37086) Full Text: DOI Link
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
Li, Chengzhi Slow-fast dynamics and its application to a biological model. (English) Zbl 1365.37064 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, 301-325 (2016). MSC: 37N25 92D25 34D15 34E13 PDFBibTeX XMLCite \textit{C. Li}, Springer Proc. Math. Stat. 157, 301--325 (2016; Zbl 1365.37064) Full Text: DOI
Bobieński, Marcin; Gavrilov, Lubomir Finite cyclicity of slow-fast Darboux systems with a two-saddle loop. (English) Zbl 1362.34048 Proc. Am. Math. Soc. 144, No. 10, 4205-4219 (2016). Reviewer: M. A. M. Alwash (Culver City) MSC: 34C07 34C37 34C23 PDFBibTeX XMLCite \textit{M. Bobieński} and \textit{L. Gavrilov}, Proc. Am. Math. Soc. 144, No. 10, 4205--4219 (2016; Zbl 1362.34048) Full Text: DOI arXiv
Wynen, Jeroen Normal forms near a symmetric planar saddle connection. (English) Zbl 1342.34057 J. Differ. Equations 260, No. 10, 7606-7633 (2016). Reviewer: Jinzhi Lei (Beijing) MSC: 34C20 37G05 37C10 34C37 PDFBibTeX XMLCite \textit{J. Wynen}, J. Differ. Equations 260, No. 10, 7606--7633 (2016; Zbl 1342.34057) Full Text: DOI
Huzak, Renato Cyclicity of the origin in slow-fast codimension 3 saddle and elliptic bifurcations. (English) Zbl 1318.34077 Discrete Contin. Dyn. Syst. 36, No. 1, 171-215 (2016). MSC: 34E15 37G15 34E20 34C23 34C26 PDFBibTeX XMLCite \textit{R. Huzak}, Discrete Contin. Dyn. Syst. 36, No. 1, 171--215 (2016; Zbl 1318.34077) Full Text: DOI
Françoise, Jean-Pierre; Xiao, Dongmei Perturbation theory of a symmetric center within Liénard equations. (English) Zbl 1387.34088 J. Differ. Equations 259, No. 6, 2408-2429 (2015). MSC: 34E10 34C05 34A34 34C14 34A05 34C08 PDFBibTeX XMLCite \textit{J.-P. Françoise} and \textit{D. Xiao}, J. Differ. Equations 259, No. 6, 2408--2429 (2015; Zbl 1387.34088) Full Text: DOI
De Maesschalck, P. Planar canards with transcritical intersections. (English) Zbl 1379.34052 Acta Appl. Math. 137, No. 1, 159-184 (2015). MSC: 34E17 34E15 34C20 34C26 34D20 PDFBibTeX XMLCite \textit{P. De Maesschalck}, Acta Appl. Math. 137, No. 1, 159--184 (2015; Zbl 1379.34052) Full Text: DOI
De Maesschalck, P.; Rebollo-Perdomo, S.; Torregrosa, J. Cyclicity of a fake saddle inside the quadratic vector fields. (English) Zbl 1314.34066 J. Differ. Equations 258, No. 2, 588-620 (2015). Reviewer: Douglas S. Shafer (Charlotte) MSC: 34C07 37G10 37G15 34D15 34C23 34C05 PDFBibTeX XMLCite \textit{P. De Maesschalck} et al., J. Differ. Equations 258, No. 2, 588--620 (2015; Zbl 1314.34066) Full Text: DOI
Huzak, Renato; De Maesschalck, P.; Dumortier, Freddy Primary birth of canard cycles in slow-fast codimension 3 elliptic bifurcations. (English) Zbl 1322.34067 Commun. Pure Appl. Anal. 13, No. 6, 2641-2673 (2014). Reviewer: Nikola Popovic (Edinburgh) MSC: 34E17 34E15 37G15 34E20 34C23 34C20 34C45 34C26 PDFBibTeX XMLCite \textit{R. Huzak} et al., Commun. Pure Appl. Anal. 13, No. 6, 2641--2673 (2014; Zbl 1322.34067) Full Text: DOI
Li, Chengzhi; Li, Jianquan; Ma, Zhien; Zhu, Huanping Canard phenomenon for an SIS epidemic model with nonlinear incidence. (English) Zbl 1303.34040 J. Math. Anal. Appl. 420, No. 2, 987-1004 (2014). Reviewer: Robert Vrabel (Trnava) MSC: 34C60 34D15 34C23 34E17 92D30 PDFBibTeX XMLCite \textit{C. Li} et al., J. Math. Anal. Appl. 420, No. 2, 987--1004 (2014; Zbl 1303.34040) Full Text: DOI
De Maesschalck, Peter; Dumortier, Freddy; Roussarie, Robert Canard-cycle transition at a fast-fast passage through a jump point. (Transition de cycles canard pour un passage rapide-rapide par un point de saut.) (English. Abridged French version) Zbl 1287.34044 C. R., Math., Acad. Sci. Paris 352, No. 1, 27-30 (2014). MSC: 34E17 34E15 34C05 PDFBibTeX XMLCite \textit{P. De Maesschalck} et al., C. R., Math., Acad. Sci. Paris 352, No. 1, 27--30 (2014; Zbl 1287.34044) Full Text: DOI
Dumortier, Freddy Canard explosion and position curves. (English) Zbl 1314.37036 Johann, Andreas (ed.) et al., Recent trends in dynamical systems. Proceedings of the international conference, Munich, Germany, January 11–13, 2012, in honor of Jürgen Scheurle on the occasion of his 60th birthday. Basel: Springer (ISBN 978-3-0348-0450-9/hbk; 978-3-0348-0451-6/ebook). Springer Proceedings in Mathematics & Statistics 35, 51-78 (2013). MSC: 37G15 34E15 PDFBibTeX XMLCite \textit{F. Dumortier}, Springer Proc. Math. Stat. 35, 51--78 (2013; Zbl 1314.37036) Full Text: DOI
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
Françoise, Jean-Pierre Poincaré-Andronov-Hopf bifurcation and the local Hilbert’s 16th problem. (English) Zbl 1273.34044 Qual. Theory Dyn. Syst. 11, No. 1, 61-77 (2012). Reviewer: Klaus R. Schneider (Berlin) MSC: 34C23 34C05 34C14 34C07 34E15 PDFBibTeX XMLCite \textit{J.-P. Françoise}, Qual. Theory Dyn. Syst. 11, No. 1, 61--77 (2012; Zbl 1273.34044) Full Text: DOI
Caubergh, Magdalena Hilbert’s sixteenth problem for polynomial Liénard equations. (English) Zbl 1272.34002 Qual. Theory Dyn. Syst. 11, No. 1, 3-18 (2012). Reviewer: Alexander Grin (Grodno) MSC: 34-02 34C07 37G15 34C20 PDFBibTeX XMLCite \textit{M. Caubergh}, Qual. Theory Dyn. Syst. 11, No. 1, 3--18 (2012; Zbl 1272.34002) Full Text: DOI Link
De Maesschalck, P.; Dumortier, F. Classical Liénard equations of degree \(n\geqslant 6\) can have \([\frac{n-1}{2}]+2\) limit cycles. (English) Zbl 1215.37038 J. Differ. Equations 250, No. 4, 2162-2176 (2011). Reviewer: M. A. M. Alwash (Culver City) MSC: 37G15 34E17 34C05 34C26 PDFBibTeX XMLCite \textit{P. De Maesschalck} and \textit{F. Dumortier}, J. Differ. Equations 250, No. 4, 2162--2176 (2011; Zbl 1215.37038) Full Text: DOI
De Maesschalck, P.; Dumortier, F. Slow-fast Bogdanov-Takens bifurcations. (English) Zbl 1236.34083 J. Differ. Equations 250, No. 2, 1000-1025 (2011). Reviewer: E. V. Shchetinina (Samara) MSC: 34E15 34C23 34C26 37G10 PDFBibTeX XMLCite \textit{P. De Maesschalck} and \textit{F. Dumortier}, J. Differ. Equations 250, No. 2, 1000--1025 (2011; Zbl 1236.34083) Full Text: DOI
Dumortier, Freddy; Roussarie, Robert Smooth normal linearization of vector fields near lines of singularities. (English) Zbl 1221.34104 Qual. Theory Dyn. Syst. 9, No. 1-2, 39-87 (2010). MSC: 34C20 34C14 34E20 PDFBibTeX XMLCite \textit{F. Dumortier} and \textit{R. Roussarie}, Qual. Theory Dyn. Syst. 9, No. 1--2, 39--87 (2010; Zbl 1221.34104) Full Text: DOI