-
1
-
-
0003130734
-
The slow passage through a Hopf bifurcation: delay, memory effects, and resonance
-
[1] Baer, S.M., Erneux, T., Rinzel, J., The slow passage through a Hopf bifurcation: delay, memory effects, and resonance. SIAM J. Appl. Math. 49 (1989), 55–71.
-
(1989)
SIAM J. Appl. Math.
, vol.49
, pp. 55-71
-
-
Baer, S.M.1
Erneux, T.2
Rinzel, J.3
-
2
-
-
51849105988
-
Slow acceleration and deacceleration through a Hopf bifurcation: Power ramps, target nucleation, and elliptic bursting
-
[2] Baer, S.M., Gaekel, E.M., Slow acceleration and deacceleration through a Hopf bifurcation: Power ramps, target nucleation, and elliptic bursting. Phys. Rev. E, 78, 2008, 036205.
-
(2008)
Phys. Rev. E
, vol.78
-
-
Baer, S.M.1
Gaekel, E.M.2
-
3
-
-
78149320153
-
Electrical waves in a one-dimensional model of cardiac tissue
-
[3] Beck, M.A., Jones, C.K.R.T., Schaeffer, D., Wechselberger, M., Electrical waves in a one-dimensional model of cardiac tissue. SIAM J. Appl. Dyn. Syst. 7 (2008), 1558–1581.
-
(2008)
SIAM J. Appl. Dyn. Syst.
, vol.7
, pp. 1558-1581
-
-
Beck, M.A.1
Jones, C.K.R.T.2
Schaeffer, D.3
Wechselberger, M.4
-
4
-
-
0001804686
-
-
E. Benoit Springer Verlag Berlin
-
[4] Benoit, E., Benoit, E., (eds.) Dynamic Bifurcations: Proceedings, Luminy 1990 Lect. Notes Math., vol. 1493, 1991, Springer Verlag, Berlin.
-
(1991)
Dynamic Bifurcations: Proceedings, Luminy 1990, Lect. Notes Math.
, vol.1493
-
-
Benoit, E.1
-
5
-
-
0001938848
-
Chasse au canard
-
[5] Benoit, E., Callot, J.F., Diener, F., Diener, M., Chasse au canard. Collect. Math. 31–32 (1981), 37–119.
-
(1981)
Collect. Math.
, vol.31-32
, pp. 37-119
-
-
Benoit, E.1
Callot, J.F.2
Diener, F.3
Diener, M.4
-
6
-
-
0002083219
-
Asymptotics, superasymptotics, hyperasymptotics
-
H. Segur S. Tanveer H. Levine Springer Verlag New York
-
[6] Berry, M.V., Asymptotics, superasymptotics, hyperasymptotics. Segur, H., Tanveer, S., Levine, H., (eds.) Asymptotics Beyond All Orders NATO ASI Series, vol. 284, 1991, Springer Verlag, New York, 1–14.
-
(1991)
Asymptotics Beyond All Orders, NATO ASI Series
, vol.284
, pp. 1-14
-
-
Berry, M.V.1
-
7
-
-
84890428688
-
Geometric desingularization of a cusp singularity in slow-fast systems with applications to Zeeman's examples
-
[7] Broer, H.W., Kaper, T.J., Krupa, M., Geometric desingularization of a cusp singularity in slow-fast systems with applications to Zeeman's examples. J. Dynam. Differential Equations 25 (2013), 925–958.
-
(2013)
J. Dynam. Differential Equations
, vol.25
, pp. 925-958
-
-
Broer, H.W.1
Kaper, T.J.2
Krupa, M.3
-
8
-
-
0002294440
-
The canard unchained or how fast/slow dynamical problems bifurcate
-
[8] Diener, M., The canard unchained or how fast/slow dynamical problems bifurcate. Math. Intelligencer 6 (1984), 38–49.
-
(1984)
Math. Intelligencer
, vol.6
, pp. 38-49
-
-
Diener, M.1
-
9
-
-
0003879016
-
Asymptotic Expansions: their Derivation and Interpretation
-
Academic Press London, New York
-
[9] Dingle, R.B., Asymptotic Expansions: their Derivation and Interpretation. 1973, Academic Press, London, New York.
-
(1973)
-
-
Dingle, R.B.1
-
10
-
-
0002336002
-
Techniques in the theory of local bifurcations: blow-up, normal forms, nilpotent bifurcations, and singular perturbations
-
D. Schlomiuk Kluwer Dordrecht
-
[10] Dumortier, F., Techniques in the theory of local bifurcations: blow-up, normal forms, nilpotent bifurcations, and singular perturbations. Schlomiuk, D., (eds.) Bifurcations and Periodic Orbits of Vector Fields NATO ASI Series C, vol. 408, 1993, Kluwer, Dordrecht, 19–73.
-
(1993)
Bifurcations and Periodic Orbits of Vector Fields, NATO ASI Series C
, vol.408
, pp. 19-73
-
-
Dumortier, F.1
-
11
-
-
4444232192
-
Topics in singularities and bifurcations of vector fields
-
Y. Ilyashenko C. Rousseau G. Sabidussi Kluwer Acad. Publ Dordrecht, NL
-
[11] Dumortier, F., De Maesschalck, P., Topics in singularities and bifurcations of vector fields. Ilyashenko, Y., Rousseau, C., Sabidussi, G., (eds.) Normal Forms, Bifurcations, and Finiteness Problems in Differential Equations NATO Sci. Ser. II Math. Phys. Chem., vol. 137, 2004, Kluwer Acad. Publ, Dordrecht, NL, 33–86.
-
(2004)
Normal Forms, Bifurcations, and Finiteness Problems in Differential Equations, NATO Sci. Ser. II Math. Phys. Chem.
, vol.137
, pp. 33-86
-
-
Dumortier, F.1
De Maesschalck, P.2
-
12
-
-
84938057841
-
Wave speeds for the FKPP equation with enhancements of the reaction function
-
[12] Dumortier, F., Kaper, T.J., Wave speeds for the FKPP equation with enhancements of the reaction function. Z. Angew. Math. Phys. 66 (2015), 607–629.
-
(2015)
Z. Angew. Math. Phys.
, vol.66
, pp. 607-629
-
-
Dumortier, F.1
Kaper, T.J.2
-
13
-
-
33750685310
-
The asymptotic critical wave speed in a family of scalar reaction–diffusion equations
-
[13] Dumortier, F., Popović, Kaper, T.J., The asymptotic critical wave speed in a family of scalar reaction–diffusion equations. J. Math. Anal. Appl. 326 (2007), 1007–1023.
-
(2007)
J. Math. Anal. Appl.
, vol.326
, pp. 1007-1023
-
-
Dumortier, F.1
Popović2
Kaper, T.J.3
-
14
-
-
33947384615
-
The critical wave speed for the FKPP equation with cut-off
-
[14] Dumortier, F., Popović, N., Kaper, T.J., The critical wave speed for the FKPP equation with cut-off. Nonlinearity 20 (2007), 855–877.
-
(2007)
Nonlinearity
, vol.20
, pp. 855-877
-
-
Dumortier, F.1
Popović, N.2
Kaper, T.J.3
-
15
-
-
77956095169
-
A geometric approach to bistable front propagation in scalar reaction–diffusion equations with cut-off
-
[15] Dumortier, F., Popović, N., Kaper, T.J., A geometric approach to bistable front propagation in scalar reaction–diffusion equations with cut-off. Physica D 239 (2010), 1984–1999.
-
(2010)
Physica D
, vol.239
, pp. 1984-1999
-
-
Dumortier, F.1
Popović, N.2
Kaper, T.J.3
-
16
-
-
0039243335
-
Canard cycles and center manifolds
-
[16] Dumortier, F., Roussarie, R., Canard cycles and center manifolds. Mem. Am. Math. Soc. 121:577 (1996), 1–100.
-
(1996)
Mem. Am. Math. Soc.
, vol.121
, Issue.577
, pp. 1-100
-
-
Dumortier, F.1
Roussarie, R.2
-
17
-
-
0001838331
-
Geometric singular perturbation theory beyond normal hyperbolicity
-
C.K.R.T. Jones A. Khibnik Springer New York
-
[17] Dumortier, F., Roussarie, R., Geometric singular perturbation theory beyond normal hyperbolicity. Jones, C.K.R.T., Khibnik, A., (eds.) Multiple-Time-Scale Dynamical Systems IMA Vol. Appl. Math., vol. 122, 2001, Springer, New York, 29–63.
-
(2001)
Multiple-Time-Scale Dynamical Systems, IMA Vol. Appl. Math.
, vol.122
, pp. 29-63
-
-
Dumortier, F.1
Roussarie, R.2
-
18
-
-
0001245411
-
Bifurcations of cuspidal loops
-
[18] Dumortier, F., Roussarie, R., Sotomayor, J., Bifurcations of cuspidal loops. Nonlinearity 10 (1997), 1369–1408.
-
(1997)
Nonlinearity
, vol.10
, pp. 1369-1408
-
-
Dumortier, F.1
Roussarie, R.2
Sotomayor, J.3
-
20
-
-
12844276566
-
Slow passage through bifurcation and limit points: Asymptotic theory and applications
-
[20] Erneux, T., Reiss, E.L., Holden, L.J., Georgiou, M., Slow passage through bifurcation and limit points: Asymptotic theory and applications. Dynamic Bifurcations Lecture Notes in Mathematics, vol. 1493, 1991, 14–28.
-
(1991)
Dynamic Bifurcations, Lecture Notes in Mathematics
, vol.1493
, pp. 14-28
-
-
Erneux, T.1
Reiss, E.L.2
Holden, L.J.3
Georgiou, M.4
-
21
-
-
0001356311
-
Persistence and smoothness of invariant manifolds for flows
-
[21] Fenichel, N., Persistence and smoothness of invariant manifolds for flows. Indiana Univ. Math. J. 21 (1971), 193–226.
-
(1971)
Indiana Univ. Math. J.
, vol.21
, pp. 193-226
-
-
Fenichel, N.1
-
22
-
-
34250627892
-
Geometrical singular perturbation theory for ordinary differential equations
-
[22] Fenichel, N., Geometrical singular perturbation theory for ordinary differential equations. J. Differential Equations 31 (1979), 53–98.
-
(1979)
J. Differential Equations
, vol.31
, pp. 53-98
-
-
Fenichel, N.1
-
23
-
-
84856287858
-
Geometric singular perturbation analysis of an autocatalator model
-
[23] Gucwa, I., Szmolyan, P., Geometric singular perturbation analysis of an autocatalator model. Discrete Contin. Dyn. Syst. Ser. S 2 (2009), 783–806.
-
(2009)
Discrete Contin. Dyn. Syst. Ser. S
, vol.2
, pp. 783-806
-
-
Gucwa, I.1
Szmolyan, P.2
-
24
-
-
84967395875
-
Geometric analysis of delayed bifurcations
-
(Ph.D. thesis) Department of Mathematics, Boston University
-
[24] Hayes, M.G., Geometric analysis of delayed bifurcations. (Ph.D. thesis), 2000, Department of Mathematics, Boston University.
-
(2000)
-
-
Hayes, M.G.1
-
25
-
-
0003537521
-
-
Springer Verlag Berlin, New York
-
[25] Hirsch, M., Pugh, C., Shub, M., Invariant Manifolds Lect. Notes in Math., vol. 583, 1977, Springer Verlag, Berlin, New York.
-
(1977)
Invariant Manifolds, Lect. Notes in Math.
, vol.583
-
-
Hirsch, M.1
Pugh, C.2
Shub, M.3
-
26
-
-
84873408825
-
Existence and stability of traveling pulses in a reaction–diffusion-mechanics system
-
[26] Holzer, M.D., Doelman, A., Kaper, T.J., Existence and stability of traveling pulses in a reaction–diffusion-mechanics system. J. Nonlinear Sci. 23 (2013), 129–177.
-
(2013)
J. Nonlinear Sci.
, vol.23
, pp. 129-177
-
-
Holzer, M.D.1
Doelman, A.2
Kaper, T.J.3
-
27
-
-
84862727240
-
A slow pushed front in a Lotka–Volterra competition model
-
[27] Holzer, M.D., Scheel, A., A slow pushed front in a Lotka–Volterra competition model. Nonlinearity 25 (2012), 2151–2179.
-
(2012)
Nonlinearity
, vol.25
, pp. 2151-2179
-
-
Holzer, M.D.1
Scheel, A.2
-
28
-
-
0002316532
-
Geometric singular perturbation theory
-
R. Johnson Springer-Verlag Berlin
-
[28] Jones, C.K.R.T., Geometric singular perturbation theory. Johnson, R., (eds.) Dynamical Systems, Montecatini Terme, 1994 Lect. Notes in Math., vol. 1609, 1995, Springer-Verlag, Berlin, 44–118.
-
(1995)
Dynamical Systems, Montecatini Terme, 1994, Lect. Notes in Math.
, vol.1609
, pp. 44-118
-
-
Jones, C.K.R.T.1
-
29
-
-
84856240719
-
Scaling in singular perturbation problems: blowing up a relaxation oscillator
-
[29] Kosiuk, I., Szmolyan, P., Scaling in singular perturbation problems: blowing up a relaxation oscillator. SIAM J. Appl. Dyn. Syst. 10 (2011), 1307–1343.
-
(2011)
SIAM J. Appl. Dyn. Syst.
, vol.10
, pp. 1307-1343
-
-
Kosiuk, I.1
Szmolyan, P.2
-
30
-
-
49749152086
-
New dynamics in cerebellar Purkinje cells: torus canards
-
[30] Kramer, M.A., Traub, R.D., Kopell, N., New dynamics in cerebellar Purkinje cells: torus canards. Phys. Rev. Lett., 101, 2008, 068103.
-
(2008)
Phys. Rev. Lett.
, vol.101
-
-
Kramer, M.A.1
Traub, R.D.2
Kopell, N.3
-
31
-
-
0036052772
-
Extending geometric singular perturbation theory to nonhyperbolic points–fold and canard points in two dimensions
-
[31] Krupa, M., Szmolyan, P., Extending geometric singular perturbation theory to nonhyperbolic points–fold and canard points in two dimensions. SIAM J. Math. Anal. 33 (2001), 286–314.
-
(2001)
SIAM J. Math. Anal.
, vol.33
, pp. 286-314
-
-
Krupa, M.1
Szmolyan, P.2
-
32
-
-
0035839416
-
Relaxation oscillation and canard explosion
-
[32] Krupa, M., Szmolyan, P., Relaxation oscillation and canard explosion. J. Differential Equations 174 (2001), 312–368.
-
(2001)
J. Differential Equations
, vol.174
, pp. 312-368
-
-
Krupa, M.1
Szmolyan, P.2
-
33
-
-
77952429290
-
Local analysis near a folded saddle–node singularity
-
[33] Krupa, M., Wechselberger, M., Local analysis near a folded saddle–node singularity. J. Differential Equations 248 (2010), 2841–2888.
-
(2010)
J. Differential Equations
, vol.248
, pp. 2841-2888
-
-
Krupa, M.1
Wechselberger, M.2
-
34
-
-
79958227982
-
-
Springer Heidelberg, New York
-
[34] Kuehn, C., Multiple Time Scale Dynamics Applied Mathematical Sciences Series, vol. 191, 2015, Springer, Heidelberg, New York.
-
(2015)
Multiple Time Scale Dynamics, Applied Mathematical Sciences Series
, vol.191
-
-
Kuehn, C.1
-
35
-
-
84902664274
-
Transonic evaporation waves in a spherically-symmetric nozzle
-
[35] Lin, X.-B., Wechselberger, M., Transonic evaporation waves in a spherically-symmetric nozzle. SIAM J. Math. An. 46 (2014), 1476–1504.
-
(2014)
SIAM J. Math. An.
, vol.46
, pp. 1476-1504
-
-
Lin, X.-B.1
Wechselberger, M.2
-
36
-
-
58149350059
-
Traveling waves for a thin liquid film with surfactant on an inclined plane
-
[36] Manukian, V., Schecter, S., Traveling waves for a thin liquid film with surfactant on an inclined plane. Nonlinearity 22 (2009), 85–122.
-
(2009)
Nonlinearity
, vol.22
, pp. 85-122
-
-
Manukian, V.1
Schecter, S.2
-
37
-
-
0000881314
-
Persistence of stability loss for dynamical bifurcations. I
-
(in Russian). [English translation: Diff. Eq., 23 (1988) 1385–1391, Plenum Pub. Corp.]
-
[37] Neishtadt, A.I., Persistence of stability loss for dynamical bifurcations. I. Differ. Uravn. 23 (1987), 2060–2067 (in Russian). [English translation: Diff. Eq., 23 (1988) 1385–1391, Plenum Pub. Corp.].
-
(1987)
Differ. Uravn.
, vol.23
, pp. 2060-2067
-
-
Neishtadt, A.I.1
-
38
-
-
0001704275
-
Persistence of stability loss for dynamical bifurcations. II
-
(in Russian). [English translation: Diff. Eq., 24 (1988) 171–176, Plenum Pub. Corp.]
-
[38] Neishtadt, A.I., Persistence of stability loss for dynamical bifurcations. II. Differ. Uravn. 24 (1988), 226–233 (in Russian). [English translation: Diff. Eq., 24 (1988) 171–176, Plenum Pub. Corp.].
-
(1988)
Differ. Uravn.
, vol.24
, pp. 226-233
-
-
Neishtadt, A.I.1
-
39
-
-
25844483339
-
A geometric analysis of logarithmic switchback phenomena,
-
[39] N. Popović, A geometric analysis of logarithmic switchback phenomena, in: HAMSA 2004: Proceedings of the International Workshop on Hysteresis and Multi-Scale Asymptotics, Cork 2004, J. Phys. Conference Series, vol. 22, 2005, pp. 164–173.
-
(2005)
HAMSA 2004: Proceedings of the International Workshop on Hysteresis and Multi-Scale Asymptotics, Cork 2004, J. Phys. Conference Series
, vol.22
, pp. 164-173
-
-
Popović, N.1
-
40
-
-
77956094477
-
Front speeds, cut-offs, and desingularization: a brief case study
-
Amer. Math. Soc. Providence, RI
-
[40] Popović, N., Front speeds, cut-offs, and desingularization: a brief case study. Fluids and Waves Contemp. Math., vol. 440, 2007, Amer. Math. Soc., Providence, RI, 187–195.
-
(2007)
Fluids and Waves, Contemp. Math.
, vol.440
, pp. 187-195
-
-
Popović, N.1
-
41
-
-
79957927597
-
A geometric analysis of front propagation in a family of degenerate reaction–diffusion equations with cut-off
-
[41] Popović, N., A geometric analysis of front propagation in a family of degenerate reaction–diffusion equations with cut-off. Z. Angew. Math. Phys. 62 (2011), 405–437.
-
(2011)
Z. Angew. Math. Phys.
, vol.62
, pp. 405-437
-
-
Popović, N.1
-
42
-
-
84868193595
-
A geometric analysis of front propagation in an integrable Nagumo equation with a linear cut-off
-
[42] Popović, N., A geometric analysis of front propagation in an integrable Nagumo equation with a linear cut-off. Physica D 241 (2012), 1976–1984.
-
(2012)
Physica D
, vol.241
, pp. 1976-1984
-
-
Popović, N.1
-
43
-
-
1942478419
-
A geometric analysis of the Lagerstrom model problem
-
[43] Popović, N., Szmolyan, P., A geometric analysis of the Lagerstrom model problem. J. Differential Equations 199 (2004), 290–325.
-
(2004)
J. Differential Equations
, vol.199
, pp. 290-325
-
-
Popović, N.1
Szmolyan, P.2
-
44
-
-
2942682726
-
Defects in oscillatory media: toward a classification
-
[44] Sandstede, B., Scheel, A., Defects in oscillatory media: toward a classification. SIAM J. Appl. Dyn. Syst. 3 (2004), 1–68.
-
(2004)
SIAM J. Appl. Dyn. Syst.
, vol.3
, pp. 1-68
-
-
Sandstede, B.1
Scheel, A.2
-
45
-
-
2942631674
-
Evans function and blow-up methods in critical eigenvalue problems
-
[45] Sandstede, B., Scheel, A., Evans function and blow-up methods in critical eigenvalue problems. Discrete Contin. Dyn. Syst. Ser. A 10 (2004), 941–964.
-
(2004)
Discrete Contin. Dyn. Syst. Ser. A
, vol.10
, pp. 941-964
-
-
Sandstede, B.1
Scheel, A.2
-
46
-
-
78049306041
-
Heteroclinic orbits in slow-fast Hamiltonian systems with slow manifold bifurcations
-
[46] Schecter, S., Sourdis, C., Heteroclinic orbits in slow-fast Hamiltonian systems with slow manifold bifurcations. J. Dynam. Differential Equations 22 (2010), 629–655.
-
(2010)
J. Dynam. Differential Equations
, vol.22
, pp. 629-655
-
-
Schecter, S.1
Sourdis, C.2
-
48
-
-
68649083754
-
Persistence of rarefactions under Dafermos regularization: blow-up and an Exchange Lemma for gain-of-stability turning points
-
[48] Schecter, S., Szmolyan, P., Persistence of rarefactions under Dafermos regularization: blow-up and an Exchange Lemma for gain-of-stability turning points. SIAM J. Appl. Dyn. Syst. 8 (2009), 822–853.
-
(2009)
SIAM J. Appl. Dyn. Syst.
, vol.8
, pp. 822-853
-
-
Schecter, S.1
Szmolyan, P.2
-
49
-
-
0001206248
-
A discussion of a certain system of differential equations with a small parameter multiplying the highest derivatives
-
[49] Shishkova, M.A., A discussion of a certain system of differential equations with a small parameter multiplying the highest derivatives. Dokl. Akad. Nauk SSSR 209 (1973), 576–579.
-
(1973)
Dokl. Akad. Nauk SSSR
, vol.209
, pp. 576-579
-
-
Shishkova, M.A.1
-
50
-
-
38248998932
-
Delayed oscillation phenomena in the FitzHugh Nagumo equation
-
[50] Su, J., Delayed oscillation phenomena in the FitzHugh Nagumo equation. J. Differential Equations 105 (1993), 180–215.
-
(1993)
J. Differential Equations
, vol.105
, pp. 180-215
-
-
Su, J.1
-
51
-
-
0347461211
-
Effects of periodic forcing on delayed bifurcations
-
[51] Su, J., Effects of periodic forcing on delayed bifurcations. J. Dynam. Differential Equations 9 (1997), 561–625.
-
(1997)
J. Dynam. Differential Equations
, vol.9
, pp. 561-625
-
-
Su, J.1
-
54
-
-
84940878688
-
Canards of folded saddle–node type I
-
[54] Vo, T., Wechselberger, M., Canards of folded saddle–node type I. SIAM J. Math. Anal. 47 (2015), 3235–3283.
-
(2015)
SIAM J. Math. Anal.
, vol.47
, pp. 3235-3283
-
-
Vo, T.1
Wechselberger, M.2
-
58
-
-
78149309138
-
Folds, canards, and shocks in advection–reaction–diffusion models
-
[58] Wechselberger, M., Pettet, G., Folds, canards, and shocks in advection–reaction–diffusion models. Nonlinearity 23 (2010), 1949–1969.
-
(2010)
Nonlinearity
, vol.23
, pp. 1949-1969
-
-
Wechselberger, M.1
Pettet, G.2
|