We. Fitzgibbon et al., FINITE DIMENSIONALITY AND UPPER SEMICONTINUITY OF THE GLOBAL ATTRACTOR OF SINGULARLY PERTURBED HODGKIN-HUXLEY SYSTEMS, Journal of differential equations, 129(1), 1996, pp. 193-237
In an effort to show that the standard Hodgkin-Huxley system approxima
tes the hyperbolic Hodgkin-Huxley system we view the hyperbolic system
as a singular perturbation of the standard system. We establish the e
xistence of global attractors for the singularly perturbed hyperbolic
system and show that they have finite fractal and Hausdorff dimensions
. We then show that the global attractors of the singularly perturbed
system converge to the global attractor for the standard system as the
small perturbation parameter decreases to zero. (C) 1996 Academic Pre
ss, Inc.