\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Primary birth of canard cycles in slow-fast codimension 3 elliptic bifurcations

Abstract Related Papers Cited by
  • In this paper we continue the study of ``large" small-amplitude limit cycles in slow-fast codimension 3 elliptic bifurcations which is initiated in [8]. Our treatment is based on blow-up and good normal forms.
    Mathematics Subject Classification: Primary: 34E15, 37G15, 34E20, 34C23, 34C26.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    P. De Maesschalck and F. Dumortier, Slow-fast Bogdanov-Takens bifurcations, J. Differential Equations, 250 (2011), 1000-1025.doi: 10.1016/j.jde.2010.07.022.

    [2]

    F. Dumortier and R. Roussarie, Birth of canard cycles, Discrete Contin. Dyn. Syst. Ser. S, 2 (2009), 723-781.doi: 10.3934/dcdss.2009.2.723.

    [3]

    P. De Maesschalck and F. Dumortier, Singular perturbations and vanishing passage through a turning point, J. Differential Equations, 248 (2010), 2294-2328.doi: 10.1016/j.jde.2009.11.009.

    [4]

    P. De Maesschalck and F. Dumortier, Canard cycles in the presence of slow dynamics with singularities, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 265-299.doi: 10.1017/S0308210506000199.

    [5]

    F. Dumortier, R. Roussarie, J. Sotomayor, and H. Zoladek, Bifurcations of Planar Vector Fields, Lecture Notes in Mathematics, 1480, Springer-Verlag, Berlin, 1991.

    [6]

    Freddy Dumortier, Compactification and desingularization of spaces of polynomial Liénard equations, J. Differential Equations, 224 (2006), 296-313.doi: 10.1016/j.jde.2005.08.011.

    [7]

    Robert Roussarie, Putting a boundary to the space of Liénard equations, Discrete Contin. Dyn. Syst., 17 (2007), 441-448.doi: 10.3934/dcds.2007.17.441.

    [8]

    R. Huzak, P. De Maesschalck and F. Dumortier, Limit cycles in slow-fast codimension 3 saddle and elliptic bifurcations, J. Differential Equations, 255 (2013), 4012-4051.doi: 10.1016/j.jde.2013.07.057.

    [9]

    Peter De Maesschalck and Freddy Dumortier, Detectable canard cycles with singular slow dynamics of any order at the turning point, Discrete Contin. Dyn. Syst., 29 (2011), 109-140.doi: 10.3934/dcds.2011.29.109.

    [10]

    P. De Maesschalck and F. Dumortier, Time analysis and entry-exit relation near planar turning points, J. Differential Equations, 215 (2005), 225-267.doi: 10.1016/j.jde.2005.01.004.

    [11]

    P. Bonckaert, P. De Maesschalck and F. Dumortier, Well adapted normal linearization in singular perturbation problems, J. Dynam. Differential Equations, 23 (2011), 115-139.doi: 10.1007/s10884-010-9191-0.

    [12]

    M. Krupa and P. Szmolyan, Relaxation oscillation and canard explosion, J. Differential Equations, 174 (2001), 312-368.doi: 10.1006/jdeq.2000.3929.

    [13]

    Daniel Panazzolo, Desingularization of nilpotent singularities in families of planar vector fields, Mem. Amer. Math. Soc., 158 (2002).doi: 10.1090/memo/0753.

    [14]

    J. Llibre, A survey on the limit cycles of the generalized polynomial Liénard differential equations, Mathematical models in engineering, biology and medicine, AIP Conf. Proc., 1124 (2009), 224-233.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(99) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return