-
1
-
-
0012104706
-
Singularity theory
-
[Arn81], Cambridge University Press, Cambridge, UK
-
[Arn81] V. I. ARNOLD, Singularity Theory, London Math. Soc. Lecture Note Ser. 53, Cambridge University Press, Cambridge, UK, 1981.
-
(1981)
London Math. Soc. Lecture Note Ser.
, vol.53
-
-
Arnold, V.I.1
-
2
-
-
0001938848
-
Chasse au canard
-
[BCDD81]
-
[BCDD81] E. BENOÎT, J. F. CALLOT, F. DIENER, AND M. DIENER, Chasse au canard, Collect. Math., 31-32 (1981), pp. 37-119.
-
(1981)
Collect. Math.
, vol.31-32
, pp. 37-119
-
-
Benoît, E.1
Callot, J.F.2
Diener, F.3
Diener, M.4
-
3
-
-
0001031806
-
3 et leur canards
-
[Ben83]
-
3 et leur canards, Astérisque, 109-110 (1983), pp. 159-191.
-
(1983)
Astérisque
, vol.109-110
, pp. 159-191
-
-
Benoît, E.1
-
5
-
-
0041402471
-
Perturbation singuliére en dimension trois: Canards en un point pseudo-singulier noeud
-
[Ben01]
-
[Ben01] E. BENOÎT, Perturbation singuliére en dimension trois: Canards en un point pseudo-singulier noeud, Bull. Soc. Math. France, 129 (2001), pp. 91-113.
-
(2001)
Bull. Soc. Math. France
, vol.129
, pp. 91-113
-
-
Benoît, E.1
-
6
-
-
3042629354
-
The forced van der Pol equation II: Canards in the reduced system
-
[BEG03]
-
[BEG03] K. BOLD, C. EDWARDS, J. GUCKENHEIMER, S. GUHARAY, K. HUFFMAN, J. HUBBARD, R. OLIVA, AND W. WECKESSER, The forced van der Pol equation II: Canards in the reduced system, SIAM J. Appl. Dyn. Syst., 2 (2003), pp. 570-608.
-
(2003)
SIAM J. Appl. Dyn. Syst.
, vol.2
, pp. 570-608
-
-
Bold, K.1
Edwards, C.2
Guckenheimer, J.3
Guharay, S.4
Huffman, K.5
Hubbard, J.6
Oliva, R.7
Weckesser, W.8
-
7
-
-
0031258126
-
Near-threshold bursting is delayed by a slow passage near a limit point
-
[BCE97]
-
[BCE97] V. BOOTH, T. W. CARR, AND T. ERNEUX, Near-threshold bursting is delayed by a slow passage near a limit point, SIAM J. Appl. Math., 57 (1997), pp. 1406-1420.
-
(1997)
SIAM J. Appl. Math.
, vol.57
, pp. 1406-1420
-
-
Booth, V.1
Carr, T.W.2
Erneux, T.3
-
8
-
-
0013630323
-
Canard explosion and excitation in a model of the Belousov-Zhabotinskii reaction
-
[BB91]
-
[BB91] M. BRøNS AND K. BAR-ELI, Canard explosion and excitation in a model of the Belousov-Zhabotinskii reaction, J. Phys. Chem., 95 (1991), pp. 8706-8713.
-
(1991)
J. Phys. Chem.
, vol.95
, pp. 8706-8713
-
-
Brøns, M.1
Bar-Eli, K.2
-
10
-
-
0042865280
-
Diffusion-induced instabilities near a canard
-
[BDE95]
-
[BDE95] F. BUCHHOLTZ, M. DOLNIK, AND I. R. EPSTEIN, Diffusion-induced instabilities near a canard, J. Phys. Chem., 99 (1995), pp. 15093-15101.
-
(1995)
J. Phys. Chem.
, vol.99
, pp. 15093-15101
-
-
Buchholtz, F.1
Dolnik, M.2
Epstein, I.R.3
-
11
-
-
0002294440
-
The canard unchained or how fast/slow dynamical problems bifurcate
-
[Die84]
-
[Die84] M. DIENER, The canard unchained or how fast/slow dynamical problems bifurcate, Math. Intelligencer, 6 (1984), pp. 38-49.
-
(1984)
Math. Intelligencer
, vol.6
, pp. 38-49
-
-
Diener, M.1
-
12
-
-
16244415882
-
Analysis of a canard mechanism by which excitatory synaptic coupling can synchronize neurons at low firing frequencies
-
[DRSE04]
-
[DRSE04] J. DROVER, J. RUBIN, J. Su, AND B. ERMENTROUT, Analysis of a canard mechanism by which excitatory synaptic coupling can synchronize neurons at low firing frequencies, SIAM J. Appl. Math., 65 (2004), pp. 69-92.
-
(2004)
SIAM J. Appl. Math.
, vol.65
, pp. 69-92
-
-
Drover, J.1
Rubin, J.2
Su, J.3
Ermentrout, B.4
-
14
-
-
0003297685
-
Relaxation oscillations including a standard chase on French ducks
-
[Eck83], Asymptotic Analysis II, Springer-Verlag, New York
-
[Eck83] W. ECKHAUS, Relaxation oscillations including a standard chase on French ducks, in Asymptotic Analysis II, Lecture Notes in Math. 985, Springer-Verlag, New York, 1983, pp. 449-494.
-
(1983)
Lecture Notes in Math.
, vol.985
, pp. 449-494
-
-
Eckhaus, W.1
-
15
-
-
34250627892
-
Geometric singular perturbation theory
-
[Fen79]
-
[Fen79] N. FENICHEL, Geometric singular perturbation theory, J. Differential Equations, 31 (1979), pp. 53-98.
-
(1979)
J. Differential Equations
, vol.31
, pp. 53-98
-
-
Fenichel, N.1
-
16
-
-
0000450921
-
Thresholds and plateaus in the Hodgkin-Huxley nerve equations
-
[FiH60]
-
[FiH60] R. FITZHUGH, Thresholds and plateaus in the Hodgkin-Huxley nerve equations, J. Gen. Physiol., 43 (1960), pp. 867-896.
-
(1960)
J. Gen. Physiol.
, vol.43
, pp. 867-896
-
-
Fitzhugh, R.1
-
17
-
-
0003263144
-
Singularities and groups in bifurcation theory
-
[GS84], Springer-Verlag, New York
-
[GS84] M. GOLUBITSKY AND D. SCHAEFFER, Singularities and Groups in Bifurcation Theory, Appl. Math. Sci. 51, Springer-Verlag, New York, 1984.
-
(1984)
Appl. Math. Sci.
, vol.51
-
-
Golubitsky, M.1
Schaeffer, D.2
-
19
-
-
0003285244
-
Nonlinear oscillations, dynamical systems and bifurcations of vector fields
-
[GH83], Springer-Verlag, New York
-
[GH83] J. GUCKENHEIMER AND P. HOLMES, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Appl. Math. Sci. 42, Springer-Verlag, New York, 1983.
-
(1983)
Appl. Math. Sci.
, vol.42
-
-
Guckenheimer, J.1
Holmes, P.2
-
20
-
-
0029258143
-
Synchrony in excitatory neural networks
-
[HMM95]
-
[HMM95] D. HANSEL, G. MATO, AND C. MEUNIER, Synchrony in excitatory neural networks, Neural Computation, 7 (1995), pp. 307-337.
-
(1995)
Neural Computation
, vol.7
, pp. 307-337
-
-
Hansel, D.1
Mato, G.2
Meunier, C.3
-
21
-
-
35649001607
-
A quantitative description of membrane current and its application to conduction and excitation in nerve
-
[HH52]
-
[HH52] A. L. HODGKIN AND A. F. HUXLEY, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. (London), 117 (1952), pp. 500-544.
-
(1952)
J. Physiol. (London)
, vol.117
, pp. 500-544
-
-
Hodgkin, A.L.1
Huxley, A.F.2
-
22
-
-
0002316532
-
Geometric singular perturbation theory
-
[Jon95], Dynamical Systems, Springer-Verlag, New York
-
[Jon95] C. K. R. T. JONES, Geometric singular perturbation theory, in Dynamical Systems, Lecture Notes in Math. 1609, Springer-Verlag, New York, 1995, pp. 44-120.
-
(1995)
Lecture Notes in Math.
, vol.1609
, pp. 44-120
-
-
Jones, C.K.R.T.1
-
23
-
-
0036052772
-
Extending geometric singular perturbation theory to nonhyperbolic points - Fold and canard points in two dimensions
-
[KS01]
-
[KS01] M. KRUPA AND P. SZMOLYAN, Extending geometric singular perturbation theory to nonhyperbolic points - fold and canard points in two dimensions, SIAM J. Math. Anal., 33 (2001), pp. 286-314.
-
(2001)
SIAM J. Math. Anal.
, vol.33
, pp. 286-314
-
-
Krupa, M.1
Szmolyan, P.2
-
24
-
-
0001834849
-
On the stability of the center for time periodic perturbations
-
[Mel63]
-
[Mel63] V. K. MELNIKOV, On the stability of the center for time periodic perturbations, Trans. Moscow Math. Soc., 12 (1963), pp. 1-57.
-
(1963)
Trans. Moscow Math. Soc.
, vol.12
, pp. 1-57
-
-
Melnikov, V.K.1
-
25
-
-
0032016741
-
The geometry of mixed-mode oscillations in the 3d-autocatalator
-
[MSLG98]
-
[MSLG98] A. MILIK, P. SZMOLYAN, H. LÖFFELMANN, AND E. G RÖLLER, The geometry of mixed-mode oscillations in the 3d-autocatalator, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8 (1998), pp. 505-519.
-
(1998)
Internat. J. Bifur. Chaos Appl. Sci. Engrg.
, vol.8
, pp. 505-519
-
-
Milik, A.1
Szmolyan, P.2
Löffelmann, H.3
Röller, E.G.4
-
26
-
-
0000489568
-
Asymptotic Methods in Singularly Perturbed Systems
-
[MKKR94], Consultants Bureau, New York
-
[MKKR94] E. F. MISHCHENKO, YU. S. KOLESOV, A. YU. KOLESOV, AND N. KH. RHOZOV, Asymptotic Methods in Singularly Perturbed Systems, Monogr. Contemp. Math., Consultants Bureau, New York, 1994.
-
(1994)
Monogr. Contemp. Math.
-
-
Mishchenko, E.F.1
Kolesov, Yu.S.2
Kolesov, A.Yu.3
Rhozov, N.Kh.4
-
27
-
-
0000069965
-
Canards in a surface oxidation reaction
-
[Moe02]
-
[Moe02] J. MOEHLIS, Canards in a surface oxidation reaction, J. Nonlinear Sci., 12 (2002), pp. 319-345.
-
(2002)
J. Nonlinear Sci.
, vol.12
, pp. 319-345
-
-
Moehlis, J.1
-
28
-
-
6344238035
-
An active pulse transmission line simulating nerve axon
-
[NAY62]
-
[NAY62] J. S. NAGUMO, S. ARIMOTO, AND S. YOSHIZAWA, An active pulse transmission line simulating nerve axon, Proc. IRE, 50 (1962), pp. 2061-2070.
-
(1962)
Proc. IRE
, vol.50
, pp. 2061-2070
-
-
Nagumo, J.S.1
Arimoto, S.2
Yoshizawa, S.3
-
29
-
-
0041362530
-
False bifurcations in chemical systems: Canards
-
[PGS91]
-
[PGS91] B. PENG, V. CÁSPÁR, AND K. SHOWALTER, False bifurcations in chemical systems: Canards, Phil. Trans. Roy. Soc. London Sect. A, 337 (1991), pp. 275-289.
-
(1991)
Phil. Trans. Roy. Soc. London Sect. A
, vol.337
, pp. 275-289
-
-
Peng, B.1
Cáspár, V.2
Showalter, K.3
-
30
-
-
0009197412
-
Mixed-mode oscillations in chemical systems
-
[PPS92]
-
[PPS92] V. PETROV, S. K. SCOTT, AND K. SHOWALTER, Mixed-mode oscillations in chemical systems, J. Chem. Phys., 97 (1992), pp. 6191-6198.
-
(1992)
J. Chem. Phys.
, vol.97
, pp. 6191-6198
-
-
Petrov, V.1
Scott, S.K.2
Showalter, K.3
-
31
-
-
0022332422
-
Excitation dynamics: Insights from simplified membrane models
-
[Rin85]
-
[Rin85] J. RINZEL, Excitation dynamics: Insights from simplified membrane models, Fed. Proc., 44 (1985), pp. 2944-2946.
-
(1985)
Fed. Proc.
, vol.44
, pp. 2944-2946
-
-
Rinzel, J.1
-
32
-
-
0344467289
-
Canard phenomenon and localization of oscillations in the Belousov-Zhabotinsky reaction with global feedback
-
[RKZE03]
-
[RKZE03] H. G. ROTSTEIN, N. KOPELL, A. M. ZHABOTINSKY, AND I. R. EPSTEIN, Canard phenomenon and localization of oscillations in the Belousov-Zhabotinsky reaction with global feedback, J. Chem. Phys., 119 (2003), pp. 8824-8832.
-
(2003)
J. Chem. Phys.
, vol.119
, pp. 8824-8832
-
-
Rotstein, H.G.1
Kopell, N.2
Zhabotinsky, A.M.3
Epstein, I.R.4
-
33
-
-
67649321652
-
Geometric singular perturbation analysis of neuronal dynamics
-
[RT02], B. Fiedler, ed., North-Holland, Amsterdam
-
[RT02] J. RUBIN AND D. TERMAN, Geometric singular perturbation analysis of neuronal dynamics, in Handbook of Dynamical Systems, Vol. 2, B. Fiedler, ed., North-Holland, Amsterdam, 2002, pp. 93-146.
-
(2002)
Handbook of Dynamical Systems
, vol.2
, pp. 93-146
-
-
Rubin, J.1
Terman, D.2
-
34
-
-
0027344291
-
Rapid synchronization through fast threshold modulation
-
[SK93]
-
[SK93] D. SOMERS AND N. KOPELL, Rapid synchronization through fast threshold modulation, Biol. Cybernet., 68 (1993), pp. 393-407.
-
(1993)
Biol. Cybernet.
, vol.68
, pp. 393-407
-
-
Somers, D.1
Kopell, N.2
-
36
-
-
0036763657
-
Extending Melnikov-theory to invariant manifolds on non-compact domains
-
[Wec02]
-
[Wec02] M. WECHSELBERGER, Extending Melnikov-theory to invariant manifolds on non-compact domains, Dyn. Syst., 17 (2002), pp. 215-233.
-
(2002)
Dyn. Syst.
, vol.17
, pp. 215-233
-
-
Wechselberger, M.1
-
37
-
-
0003915742
-
-
[Wec98], Thesis, Vienna, University of Technology, Vienna, Austria
-
3, Thesis, Vienna, University of Technology, Vienna, Austria, 1998.
-
(1998)
3
-
-
Wechselberger, M.1
|