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 ...
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
[74] T.J. Kaper <strong>and</strong> C.K.R.T. J<strong>one</strong>s. A primer on the exchange lemma for <strong>fast</strong><strong>slow</strong><br />
systems. in: Multiple-Time-Scale Dynamical Systems, IMA Vol. 122:65–<br />
88, 2001.<br />
[75] J. Kevorkian <strong>and</strong> J.D. Cole. Multiple Scale <strong>and</strong> Singular Perturbation Methods.<br />
Springer, 1996.<br />
[76] M.T.M. Koper. Bifurcations of mixed-mode oscillations in a three-variable<br />
autonomous Van der Pol-Duffing model <strong>with</strong> a cross-shaped phase diagram.<br />
Physica D, 80:72–94, 1995.<br />
[77] B. Krauskopf, H.M. Osinga, E.J. Doedel, M.E. Henderson, J. Guckenheimer,<br />
A. Vladimirsky, M. Dellnitz, <strong>and</strong> O. Junge. A survey of methods<br />
for computing (un)stable manifolds of vector fields. Int. J. Bifurcation <strong>and</strong><br />
Chaos, 15(3):763–791, 2005.<br />
[78] B. Krauskopf <strong>and</strong> T. Riess. A Lin’s method approach to finding <strong>and</strong> continuing<br />
heteroclinic connections involving periodic orbits. Nonlinearity,<br />
21(8):1655–1690, 2008.<br />
[79] T. Krogh-Madsen, L. Glass, E. Doedel, <strong>and</strong> M. Guevara. Apparent discontinuities<br />
in the phase-setting response of cardiac pacemakers. J. Theor.<br />
Biol., 230:499–519, 2004.<br />
[80] M. Krupa, N. Popovic, <strong>and</strong> N. Kopell. Mixed-mode oscillations in three<br />
<strong>time</strong>-<strong>scale</strong> systems: A prototypical example. SIAM J. Applied Dynamical<br />
Systems, 7(2), 2008.<br />
[81] M. Krupa, N. Popovic, N. Kopell, <strong>and</strong> H.G. Rotstein. Mixed-mode oscillations<br />
in a three <strong>time</strong>-<strong>scale</strong> model for the dopaminergic neuron. Chaos, 18,<br />
2008.<br />
[82] M. Krupa, B. S<strong>and</strong>stede, <strong>and</strong> P. Szmolyan. Fast <strong>and</strong> <strong>slow</strong> waves in the<br />
FitzHugh-Nagumo equation. Journal of Differential Equations, 133:49–97,<br />
1997.<br />
[83] M. Krupa <strong>and</strong> P. Szmolyan. Extending geometric singular perturbation<br />
theory to nonhyperbolic points - fold <strong>and</strong> canard points in <strong>two</strong> dimensions.<br />
SIAM J. Math. Anal., 33(2):286–314, 2001.<br />
[84] M. Krupa <strong>and</strong> P. Szmolyan. Extending <strong>slow</strong> manifolds near transcritical<br />
<strong>and</strong> pitchfork singularities. Nonlinearity, 14:1473–1491, 2001.<br />
174