A geometric approach to singular perturbation problems with applications to nerve impulse equations

Carpenter, 1977, Periodic solutions of nerve impulse equations, J. Math. Anal. Appl., 10.1016/0022-247X(77)90235-9

Carpenter, 1974, Traveling wave solutions of nerve impulse equations

Casten, 1975, Perturbation analysis of an approximation to Hodgkin-Huxley theory, Quart. Appl. Math., 32, 365, 10.1090/qam/445095

Churchill, 1973, Invariant sets which carry cohomology, J. Differential Equations, 13, 523, 10.1016/0022-0396(73)90010-7

Churchill, 1972, Isolated invariant sets in compact metric spaces, J. Differential Equations, 12, 330, 10.1016/0022-0396(72)90036-8

Coddington, 1955

Conley, 1973

Conley, 1972, On a generalization of the Morse index, Ord. Diff. Eq., 27, 10.1016/B978-0-12-743650-0.50008-3

Conley, 1973

Conley, 1968, The retrograde circular solutions of the restricted 3-body problem via a submanifold convex to a flow, SIAM J. Appl. Math., 16, 620, 10.1137/0116050

Conley, 1971, Isolated invariant sets and isolating blocks, Trans. Amer. Math. Soc., 158, 35, 10.1090/S0002-9947-1971-0279830-1

Conley, 1973, On the structure of magneto-hydrodynamic shock waves, MRC Report No. 1336

Cronin, 1964, Fixed Points and Topological Degree in Nonlinear Analysis, Vol. 11

Easton, 1975, Isolating blocks and symbolic dynamics, J. Differential Equations, 17, 96, 10.1016/0022-0396(75)90037-6

Evans, 1972, Nerve axon equations I–IV, Indiana Univ. Math. J., 21, 877, 10.1512/iumj.1972.21.21071

Evans, 1972, Nerve axon equations I–IV, Indiana Univ. Math. J., 22, 75, 10.1512/iumj.1973.22.22009

Evans, 1972, Nerve axon equations I–IV, Indiana Univ. Math. J., 22, 577, 10.1512/iumj.1973.22.22048

Evans, 1970, Solutions to axon equations, Biophysical J., 10, 1090, 10.1016/S0006-3495(70)86355-X

FitzHugh, 1961, Impulses and physiological states in theoretical models of nerve membrane, Biophysical J., 1, 445, 10.1016/S0006-3495(61)86902-6

FitzHugh, 1960, Thresholds and plateaus in the Hodgkin-Huxley nerve equations, J. Gen. Physiol., 43, 867, 10.1085/jgp.43.5.867

Hartman, 1964

S. Hasting, On travelling wave solutions of the Hodgkin-Huxley equations, Arch. Rat. Mech. Anal., to appear.

Hastings, 1974, The existence of periodic solutions to Nagumo's equations, Quart. J. Math. Oxford, 25, 369, 10.1093/qmath/25.1.369

Hodgkin, 1952, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol., 117, 500, 10.1113/jphysiol.1952.sp004764

Luria, 1975

Montgomery, 1973, Cohomology of invariant sets under perturbation, J. Differential Equations, 13, 257, 10.1016/0022-0396(73)90018-1

McKean, 1970, Nagumo's equation, Adv. in Math., 4, 209, 10.1016/0001-8708(70)90023-X

Nagumo, 1964, An active pulse transmission line simulating nerve axon, 50, 2061

Nemytskii, 1960

Noble, 1966, Application of Hodgkin-Huxley equations to excitable tissues, Physiol. Reviews, 46, 1, 10.1152/physrev.1966.46.1.1

Rinzel, 1973, Traveling wave solutions of a nerve conduction equation, Biophysical J., 13, 1313, 10.1016/S0006-3495(73)86065-5

Smart, 1974

Smoller, 1972, Shock waves as limits of progressive wave solutions of higher-order equations, II, Comm. Pure Appl. Math., 25, 133, 10.1002/cpa.3160250203

Smoller, 1972, Viscosity matrices for two-dimensional nonlinear hyperbolic systems, II, Amer. J. Math., 94, 631, 10.2307/2373748

Stevens, 1966

Tasaki, 1957, Demonstration of two stable potential states in the giant squid axon under tetraethylammonium chloride, J. Gen. Physiol., 40, 859, 10.1085/jgp.40.6.859

Thom, 1972

Troy, 1974, Oscillation phenomena in the Hodgkin-Huxley equations

Wazewski, 1947, Sur un principe topologique de l'examen de l'allure asymptotique des intégrales des équations différentielles ordinaires, Ann. Soc. Polon. Math., 20, 279

Wilson, 1973, Lyapunov functions and isolating blocks, J. Differential Equations, 13, 106, 10.1016/0022-0396(73)90034-X

Zeeman, 1973, Differential equations for the heartbeat and nerve impulse, 683