Fitzhugh

Excitable media are some of tire most commonly observed reaction-diffusion systems in nature. An excitable system possesses a stable fixed point which responds to perturbations in a characteristic way small perturbations return quickly to tire fixed point, while larger perturbations tliat exceed a certain tlireshold value make a long excursion in concentration phase space before tire system returns to tire stable state. In many physical systems tliis behaviour is captured by tire dynamics of two concentration fields, a fast activator variable u witli cubic nullcline and a slow inhibitor variable u witli linear nullcline [31]. The FitzHugh-Nagumo equation [34], derived as a simple model for nerve impulse propagation but which can also apply to a chemical reaction scheme [35], is one of tire best known equations witli such activator-inlribitor kinetics ... 

Figure C3.6.7 Cubic (jir = 0) and linear (r = 0) nullclines for tire FitzHugh-Nagumo equation, (a) The excitable domain showing trajectories resulting from sub- and super-tlireshold excitations, (b) The oscillatory domain showing limit cycle orbits small inner limit cycle close to Hopf point large outer limit cycle far from Hopf point.

Figure C3.6.8 (a) A growing ring of excitation in an excitable FitzHugh-Nagumo medium, (b) A spiral wave in tlie same system.

This complex Ginzburg-Landau equation describes the space and time variations of the amplitude A on long distance and time scales detennined by the parameter distance from the Hopf bifurcation point. The parameters a and (5 can be detennined from a knowledge of the parameter set p and the diffusion coefficients of the reaction-diffusion equation. For example, for the FitzHugh-Nagumo equation we have a = (D - P... 

Williams MW, Fuyat HN, Fitzhugh OG. 1959. The subacute toxicity of four organic phosphates to dogs. Toxicology 1 1-7. 

The FitzHugh-Nagumo (FHN) model [82] is a simplification of the HH model and involves a tunnel diode (Fig. 23). 

Fitzhugh DJ, Naik S, Gonzalez E, Caughman SW, Hwang ST. CC chemokine receptor 6 (CCR6) is a marker for memory T cells that arrest on activated human dermal micro vascular endothelium under shear stress. J Invest Dermatol 2000 115(2) 332. 

When DDT is fed to animals, even in small quantities, there is an accumulation of the compound in the tissues, particularly the fat. Telford and Guthrie (18), Orr and Mott (13), Woodward et al. (20, 21), and Laug and Fitzhugh (9) have demonstrated that DDT will accumulate in certain tissues and in milk fat of domestic and laboratory animals. Marsden and Bird (12) found that DDT was toxic to turkeys in concentrations above 0.075% of the diet, and that turkeys fed the insecticide for 7 to 8 weeks stored DDT in their fat at concentrations ranging from 4 to 8 times that in the diet. Rubin et al. (14) reported that hens fed 0.062% DDT in their diet for 12 weeks showed reduced egg production with lowered hatchability. At one half this concentration there was a detrimental effect on egg production, but hatchability was not seriously affected. The hens were killed by doses of 0.125% DDT. The insecticide was found in the eggs in quantities much smaller than in the body fat. Harris et al. (8) have shown that DDT will accumulate in considerable quantities in the fat of lambs fed DDT-treated hay. Small amounts of the insecticide were found in other tissues. 

Carter and Fitzhugh (2, 5) have summarized the results of experiments on domestic... 

Fitzhugh, E. W. (1986), Lead read and minium, in Feller, R. L. (ed.), Artists Pigments A Handbook of Their History and Characteristics, Vol. 1, National Gallery of Art, Washington, DC. 

Sayre, E. V., Harbottle, G., Stoenner, R. W., Washburn, W., Olin, S., Fitzhugh, W., The Carbon 14 Dating of ao Iron Bloom Associated with the Voyages of Sir Martin Frobisher, Chapter 22 in this book. 

WILLIAM FITZHUGH—Smithsonian Institution, Department of Anthropology, Washington, D.C. 20560... 

Fitzhugh and Nelson (19) found that oxalic acid up to 1.2% of the diet did not affect growth or mortality rate of rats fed oxalic acid for 1 year. Microscopic pathological examination showed no major visceral damage, but some of the rats showed slight periportal hypertrophy of the hepatic cells along with slight centrolobular atrophy. 

Jenner, P., Hagan, E., Taylor, J., Cook, E. and Fitzhugh, O. (1964). Food flavorings and compounds of related structure. I. Acute oral toxicity. Food. Cosmet. Toxicol. 2 327-343. 

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