-
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.
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., (). Google Scholar |
[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.
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.
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.
doi: doi:10.1017/S0308210506000199. |
[8] |
F. Dumortier, Slow divergence integral and balanced canard solutions,, Qualitative Theory and Dynamical Systems, (). Google Scholar |
[9] |
F. Dumortier, Compactification and desingularization of spaces of polynomial Liénard equations,, J. Differential Equations, 224 (2006), 296.
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.
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.
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.
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., (). Google Scholar |
[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.
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.
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.
doi: doi:10.1017/S0308210506000199. |
[8] |
F. Dumortier, Slow divergence integral and balanced canard solutions,, Qualitative Theory and Dynamical Systems, (). Google Scholar |
[9] |
F. Dumortier, Compactification and desingularization of spaces of polynomial Liénard equations,, J. Differential Equations, 224 (2006), 296.
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.
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.
doi: doi:10.3934/dcds.2007.17.441. |
[1] |
Mats Gyllenberg, Yan Ping. The generalized Liénard systems. Discrete & Continuous Dynamical Systems - A, 2002, 8 (4) : 1043-1057. doi: 10.3934/dcds.2002.8.1043 |
[2] |
Long Wei, Zhijun Qiao, Yang Wang, Shouming Zhou. Conserved quantities, global existence and blow-up for a generalized CH equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1733-1748. doi: 10.3934/dcds.2017072 |
[3] |
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 & Continuous Dynamical Systems - A, 2010, 26 (1) : 43-61. doi: 10.3934/dcds.2010.26.43 |
[4] |
Haitao Yang, Yibin Chang. On the blow-up boundary solutions of the Monge -Ampére equation with singular weights. Communications on Pure & Applied Analysis, 2012, 11 (2) : 697-708. doi: 10.3934/cpaa.2012.11.697 |
[5] |
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 & Applied Analysis, 2020, 19 (2) : 923-939. doi: 10.3934/cpaa.2020042 |
[6] |
Akmel Dé Godefroy. Existence, decay and blow-up for solutions to the sixth-order generalized Boussinesq equation. Discrete & Continuous Dynamical Systems - A, 2015, 35 (1) : 117-137. doi: 10.3934/dcds.2015.35.117 |
[7] |
Zhaoyang Yin. Well-posedness and blow-up phenomena for the periodic generalized Camassa-Holm equation. Communications on Pure & Applied Analysis, 2004, 3 (3) : 501-508. doi: 10.3934/cpaa.2004.3.501 |
[8] |
Min Zhu, Ying Wang. Blow-up of solutions to the periodic generalized modified Camassa-Holm equation with varying linear dispersion. Discrete & Continuous Dynamical Systems - A, 2017, 37 (1) : 645-661. doi: 10.3934/dcds.2017027 |
[9] |
Xi Tu, Zhaoyang Yin. Local well-posedness and blow-up phenomena for a generalized Camassa-Holm equation with peakon solutions. Discrete & Continuous Dynamical Systems - A, 2016, 36 (5) : 2781-2801. doi: 10.3934/dcds.2016.36.2781 |
[10] |
Jinlu Li, Zhaoyang Yin. Well-posedness and blow-up phenomena for a generalized Camassa-Holm equation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5493-5508. doi: 10.3934/dcds.2016042 |
[11] |
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 & Applied Analysis, 2016, 15 (6) : 2509-2526. doi: 10.3934/cpaa.2016047 |
[12] |
Alberto Bressan, Massimo Fonte. On the blow-up for a discrete Boltzmann equation in the plane. Discrete & Continuous Dynamical Systems - A, 2005, 13 (1) : 1-12. doi: 10.3934/dcds.2005.13.1 |
[13] |
Jie Xu, Yu Miao, Jicheng Liu. Strong averaging principle for slow-fast SPDEs with Poisson random measures. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2233-2256. doi: 10.3934/dcdsb.2015.20.2233 |
[14] |
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 |
[15] |
Yong Xu, Bin Pei, Rong Guo. Stochastic averaging for slow-fast dynamical systems with fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2257-2267. doi: 10.3934/dcdsb.2015.20.2257 |
[16] |
Renato Huzak. Cyclicity of the origin in slow-fast codimension 3 saddle and elliptic bifurcations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (1) : 171-215. doi: 10.3934/dcds.2016.36.171 |
[17] |
Luca Dieci, Cinzia Elia. Smooth to discontinuous systems: A geometric and numerical method for slow-fast dynamics. Discrete & Continuous Dynamical Systems - B, 2018, 23 (7) : 2935-2950. doi: 10.3934/dcdsb.2018112 |
[18] |
Guangyu Xu, Jun Zhou. Global existence and blow-up of solutions to a singular Non-Newton polytropic filtration equation with critical and supercritical initial energy. Communications on Pure & Applied Analysis, 2018, 17 (5) : 1805-1820. doi: 10.3934/cpaa.2018086 |
[19] |
Shouming Zhou, Chunlai Mu, Liangchen Wang. Well-posedness, blow-up phenomena and global existence for the generalized $b$-equation with higher-order nonlinearities and weak dissipation. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 843-867. doi: 10.3934/dcds.2014.34.843 |
[20] |
Tetsuya Ishiwata, Shigetoshi Yazaki. A fast blow-up solution and degenerate pinching arising in an anisotropic crystalline motion. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 2069-2090. doi: 10.3934/dcds.2014.34.2069 |
2018 Impact Factor: 1.143
Tools
Metrics
Other articles
by authors
[Back to Top]