-
Previous Article
Time-dependent attractor for the Oscillon equation
- DCDS Home
- This Issue
-
Next Article
Morphisms of discrete dynamical systems
Detectable canard cycles with singular slow dynamics of any order at the turning point
1. | Hasselt University, Campus Diepenbeek, Agoralaan-Gebouw D, B-3590 Diepenbeek, Belgium |
2. | Hasselt University, Campus Diepenbeek, Agoralaan gebouw D, B-3590 Diepenbeek, Belgium |
References:
[1] |
P. Bonckaert, Partially hyperbolic fixed points with constraints, Trans. Amer. Math. Soc., 348 (1996), 997-1011.
doi: doi:10.1090/S0002-9947-96-01469-9. |
[2] |
P. Bonckaert, P. De Maesschalck and F. Dumortier, Well adapted normal linearization in singular perturbation problems,, preprint., ().
|
[3] |
P. De Maesschalck and F. Dumortier, Singular perturbations and vanishing passage through a turning point,, J. Differential Equations, ().
doi: doi:10.1016/j.jde.2009.11.009. |
[4] |
P. De Maesschalck and F. Dumortier, Slow-fast Bogdanov-Takens bifurcations,, J. Differential Equations, ().
doi: doi:10.1016/j.jde.2010.07.022. |
[5] |
P. De Maesschalck and F. Dumortier, Time analysis and entry-exit relation near planar turning points, J. Differential Equations, 215 (2005), 225-267.
doi: doi:10.1016/j.jde.2005.01.004. |
[6] |
P. De Maesschalck and F. Dumortier, Canard solutions at non-generic turning points, Trans. Amer. Math. Soc., 358 (2006), 2291-2334.
doi: doi:10.1090/S0002-9947-05-03839-0. |
[7] |
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: doi:10.1017/S0308210506000199. |
[8] |
F. Dumortier, Slow divergence integral and balanced canard solutions,, Qualitative Theory and Dynamical Systems, ().
|
[9] |
F. Dumortier, Compactification and desingularization of spaces of polynomial Liénard equations, J. Differential Equations, 224 (2006), 296-313.
doi: doi:10.1016/j.jde.2005.08.011. |
[10] |
M. Krupa and P. Szmolyan, Relaxation oscillation and canard explosion, J. Differential Equations, 174 (2001), 312-368.
doi: doi:10.1006/jdeq.2000.3929. |
[11] |
D. Panazzolo, Desingularization of nilpotent singularities in families of planar vector fields, Mem. Amer. Math. Soc., 158 (2002). |
[12] |
R. Roussarie, Putting a boundary to the space of Liénard equations, Discrete Contin. Dyn. Syst., 17 (2007), 441-448.
doi: doi:10.3934/dcds.2007.17.441. |
show all references
References:
[1] |
P. Bonckaert, Partially hyperbolic fixed points with constraints, Trans. Amer. Math. Soc., 348 (1996), 997-1011.
doi: doi:10.1090/S0002-9947-96-01469-9. |
[2] |
P. Bonckaert, P. De Maesschalck and F. Dumortier, Well adapted normal linearization in singular perturbation problems,, preprint., ().
|
[3] |
P. De Maesschalck and F. Dumortier, Singular perturbations and vanishing passage through a turning point,, J. Differential Equations, ().
doi: doi:10.1016/j.jde.2009.11.009. |
[4] |
P. De Maesschalck and F. Dumortier, Slow-fast Bogdanov-Takens bifurcations,, J. Differential Equations, ().
doi: doi:10.1016/j.jde.2010.07.022. |
[5] |
P. De Maesschalck and F. Dumortier, Time analysis and entry-exit relation near planar turning points, J. Differential Equations, 215 (2005), 225-267.
doi: doi:10.1016/j.jde.2005.01.004. |
[6] |
P. De Maesschalck and F. Dumortier, Canard solutions at non-generic turning points, Trans. Amer. Math. Soc., 358 (2006), 2291-2334.
doi: doi:10.1090/S0002-9947-05-03839-0. |
[7] |
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: doi:10.1017/S0308210506000199. |
[8] |
F. Dumortier, Slow divergence integral and balanced canard solutions,, Qualitative Theory and Dynamical Systems, ().
|
[9] |
F. Dumortier, Compactification and desingularization of spaces of polynomial Liénard equations, J. Differential Equations, 224 (2006), 296-313.
doi: doi:10.1016/j.jde.2005.08.011. |
[10] |
M. Krupa and P. Szmolyan, Relaxation oscillation and canard explosion, J. Differential Equations, 174 (2001), 312-368.
doi: doi:10.1006/jdeq.2000.3929. |
[11] |
D. Panazzolo, Desingularization of nilpotent singularities in families of planar vector fields, Mem. Amer. Math. Soc., 158 (2002). |
[12] |
R. Roussarie, Putting a boundary to the space of Liénard equations, Discrete Contin. Dyn. Syst., 17 (2007), 441-448.
doi: doi:10.3934/dcds.2007.17.441. |
[1] |
Liang Zhao, Jianhe Shen. Canards and homoclinic orbits in a slow-fast modified May-Holling-Tanner predator-prey model with weak multiple Allee effect. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022018 |
[2] |
Mats Gyllenberg, Yan Ping. The generalized Liénard systems. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 1043-1057. doi: 10.3934/dcds.2002.8.1043 |
[3] |
Long Wei, Zhijun Qiao, Yang Wang, Shouming Zhou. Conserved quantities, global existence and blow-up for a generalized CH equation. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 1733-1748. doi: 10.3934/dcds.2017072 |
[4] |
Justin Holmer, Chang Liu. Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity II: Supercritical blow-up profiles. Communications on Pure and Applied Analysis, 2021, 20 (1) : 215-242. doi: 10.3934/cpaa.2020264 |
[5] |
Bouthaina Abdelhedi, Hatem Zaag. Single point blow-up and final profile for a perturbed nonlinear heat equation with a gradient and a non-local term. Discrete and Continuous Dynamical Systems - S, 2021, 14 (8) : 2607-2623. doi: 10.3934/dcdss.2021032 |
[6] |
José M. Arrieta, Raúl Ferreira, Arturo de Pablo, Julio D. Rossi. Stability of the blow-up time and the blow-up set under perturbations. Discrete and Continuous Dynamical Systems, 2010, 26 (1) : 43-61. doi: 10.3934/dcds.2010.26.43 |
[7] |
Fangfang Jiang, Junping Shi, Qing-guo Wang, Jitao Sun. On the existence and uniqueness of a limit cycle for a Liénard system with a discontinuity line. Communications on Pure and Applied Analysis, 2016, 15 (6) : 2509-2526. doi: 10.3934/cpaa.2016047 |
[8] |
Xiumei Deng, Jun Zhou. Global existence and blow-up of solutions to a semilinear heat equation with singular potential and logarithmic nonlinearity. Communications on Pure and Applied Analysis, 2020, 19 (2) : 923-939. doi: 10.3934/cpaa.2020042 |
[9] |
Haitao Yang, Yibin Chang. On the blow-up boundary solutions of the Monge -Ampére equation with singular weights. Communications on Pure and Applied Analysis, 2012, 11 (2) : 697-708. doi: 10.3934/cpaa.2012.11.697 |
[10] |
Akmel Dé Godefroy. Existence, decay and blow-up for solutions to the sixth-order generalized Boussinesq equation. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 117-137. doi: 10.3934/dcds.2015.35.117 |
[11] |
Zhaoyang Yin. Well-posedness and blow-up phenomena for the periodic generalized Camassa-Holm equation. Communications on Pure and Applied Analysis, 2004, 3 (3) : 501-508. doi: 10.3934/cpaa.2004.3.501 |
[12] |
Wenxia Chen, Jingyi Liu, Danping Ding, Lixin Tian. Blow-up for two-component Camassa-Holm equation with generalized weak dissipation. Communications on Pure and Applied Analysis, 2020, 19 (7) : 3769-3784. doi: 10.3934/cpaa.2020166 |
[13] |
Min Zhu, Ying Wang. Blow-up of solutions to the periodic generalized modified Camassa-Holm equation with varying linear dispersion. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 645-661. doi: 10.3934/dcds.2017027 |
[14] |
Xi Tu, Zhaoyang Yin. Local well-posedness and blow-up phenomena for a generalized Camassa-Holm equation with peakon solutions. Discrete and Continuous Dynamical Systems, 2016, 36 (5) : 2781-2801. doi: 10.3934/dcds.2016.36.2781 |
[15] |
Jinlu Li, Zhaoyang Yin. Well-posedness and blow-up phenomena for a generalized Camassa-Holm equation. Discrete and Continuous Dynamical Systems, 2016, 36 (10) : 5493-5508. doi: 10.3934/dcds.2016042 |
[16] |
Alberto Bressan, Massimo Fonte. On the blow-up for a discrete Boltzmann equation in the plane. Discrete and Continuous Dynamical Systems, 2005, 13 (1) : 1-12. doi: 10.3934/dcds.2005.13.1 |
[17] |
Jie Xu, Yu Miao, Jicheng Liu. Strong averaging principle for slow-fast SPDEs with Poisson random measures. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 2233-2256. doi: 10.3934/dcdsb.2015.20.2233 |
[18] |
Alexandre Vidal. Periodic orbits of tritrophic slow-fast system and double homoclinic bifurcations. Conference Publications, 2007, 2007 (Special) : 1021-1030. doi: 10.3934/proc.2007.2007.1021 |
[19] |
Yong Xu, Bin Pei, Rong Guo. Stochastic averaging for slow-fast dynamical systems with fractional Brownian motion. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 2257-2267. doi: 10.3934/dcdsb.2015.20.2257 |
[20] |
Renato Huzak. Cyclicity of the origin in slow-fast codimension 3 saddle and elliptic bifurcations. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 171-215. doi: 10.3934/dcds.2016.36.171 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]