multiple time scale dynamics with two fast variables and one slow ...
multiple time scale dynamics with two fast variables and one slow ...
multiple time scale dynamics with two fast variables and one slow ...
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[62] S.P. Hastings. Some mathematical problems from neurobiology. The American<br />
Mathematical Monthly, 82(9):881–895, 1975.<br />
[63] S.P. Hastings. On the existence of homoclinic <strong>and</strong> periodic orbits in the<br />
fitzhugh-nagumo equations. Quart. J. Math. Oxford, 2(27):123–134, 1976.<br />
[64] M.W. Hirsch, C.C. Pugh, <strong>and</strong> M. Shub. Invariant Manifolds. Springer, 1977.<br />
[65] A.L. Hodgin <strong>and</strong> A.F. Huxley. A quantitative description of membrane<br />
current <strong>and</strong> its application to conduction <strong>and</strong> excitation in nerve. J. Physiol.,<br />
117:500–505, 1952.<br />
[66] Waterloo Maple Inc. Maple 12. http://www.maplesoft.com/, 2008.<br />
[67] J. Jalics, M. Krupa, <strong>and</strong> H.G. Rotstein. A novel canard-based mechanism<br />
for mixed-mode oscillations in a neuronal model. preprint, 2008.<br />
[68] C. J<strong>one</strong>s <strong>and</strong> N. Kopell. Tracking invariant manifolds <strong>with</strong> differential<br />
forms in singularly perturbed systems. Journal of Differential Equations,<br />
pages 64–88, 1994.<br />
[69] C. J<strong>one</strong>s, N. Kopell, <strong>and</strong> R. Langer. Construction of the FitzHugh-Nagumo<br />
pulse using differential forms. in: Multiple-Time-Scale Dynamical Systems,<br />
pages 101–113, 2001.<br />
[70] C.K.R.T. J<strong>one</strong>s. Stability of the travelling wave solution of the fitzhughnagumo<br />
system. Transactions of the American Mathematical Society,<br />
286(2):431–469, 1984.<br />
[71] C.K.R.T. J<strong>one</strong>s. Geometric Singular Perturbation Theory: in Dynamical Systems<br />
(Montecatini Terme, 1994). Springer, 1995.<br />
[72] C.K.R.T. J<strong>one</strong>s, T.J. Kaper, <strong>and</strong> N. Kopell. Tracking invariant manifolds<br />
up tp exp<strong>one</strong>ntially small errors. SIAM Journal of Mathematical Analysis,<br />
27(2):558–577, 1996.<br />
[73] T.J. Kaper. An introduction to geometric methods <strong>and</strong> dynamical systems<br />
theory for singular perturbation problems. analyzing multi<strong>scale</strong> phenomena<br />
using singular perturbation methods. Proc. Sympos. Appl. Math.,<br />
56:85–131, 1999.<br />
173