{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T22:10:36Z","timestamp":1781561436255,"version":"3.54.5"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,12]]},"abstract":"<jats:p> The four-dimensional Hodgkin\u2013Huxley equations are considered as the prototype for description of neural pulse propagation. Their mathematical complexity and sophistication prompted a simplified two-dimensional model, the FitzHugh\u2013Nagumo equations, which display many of the former's dynamical features. Numerical and mathematical analysis are employed to demonstrate that the FitzHugh\u2013Nagumo equations can provide quantitative predictions in close agreement with the Hodgkin\u2013Huxley equations. The two most important parameters of a neural pulse are its speed c(T) and pulse height v<jats:sub> max <\/jats:sub> (T) and so numerical computations of these quantities predicted by the Hodgkin\u2013Huxley equations are given over the entire temperature range T for stability of a neural pulse. Similarly, the FitzHugh\u2013Nagumo equations are parameterized by two dimensionless quantities: a which determines the dynamics of the pulse front, and b whose departure from zero tailors the front to form the resultant pulse. Parallel computations are presented for the FitzHugh\u2013Nagumo pulse whose relative simplicity permits analytic determination to close approximation of the dimensionless speed \u03b8(a, b) and pulse height V<jats:sub> max <\/jats:sub>(a, b). It is shown that the two models are numerically identified by scaling according to c = 4904 \u03b8 cm\/sec and v<jats:sub> max <\/jats:sub> = 115 V<jats:sub> max <\/jats:sub> mV where the numbers are a consequence of the experimental parameter values inherent to the Hodgkin\u2013Huxley equations. With this connection, at a given temperature the Hodgkin\u2013Huxley speed and pulse height determine unique values for the two FitzHugh\u2013Nagumo parameters a and b. Approximate analytic solution for \u03b8(a, b) allows construction of a three-dimensional [a, b, \u03b8] state plot upon which a unique ridge defines, as a function of temperature, the speed and associated pulse height predicted by the Hodgkin\u2013Huxley equations. The generality of the state plot suggests its application to other conductance models. Comparison of the Hodgkin\u2013Huxley with the FitzHugh\u2013Nagumo models highlight the quantitative limitations of the latter in the region of the minimum characterizing the back portion of the pulse. To overcome this limitation would require analytic extension of the FitzHugh\u2013Nagumo dynamics to higher dimensionality. <\/jats:p>","DOI":"10.1142\/s0218127405014349","type":"journal-article","created":{"date-parts":[[2006,3,3]],"date-time":"2006-03-03T06:45:38Z","timestamp":1141368338000},"page":"3851-3866","source":"Crossref","is-referenced-by-count":12,"title":["A COMPARATIVE STUDY OF THE HODGKIN\u2013HUXLEY AND FITZHUGH\u2013NAGUMO MODELS OF NEURON PULSE PROPAGATION"],"prefix":"10.1142","volume":"15","author":[{"given":"PAUL E.","family":"PHILLIPSON","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Theoretische Chemie und Molekulare Strukturbiologie, Universit\u00e4t Wien, W\u00e4hringerstra\u00dfe 17, A-1090 Wien, Austria"},{"name":"Austrian Academy of Sciences, Dr. Ignaz Seipel-Platz 2, A-1010 Wien, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"PETER","family":"SCHUSTER","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Theoretische Chemie und Molekulare Strukturbiologie, Universit\u00e4t Wien, W\u00e4hringerstra\u00dfe 17, A-1090 Wien, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1162\/08997660360675017"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/445095"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(66)86679-1"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/0142017"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1137\/0107037"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(61)86902-6"},{"key":"rf7","unstructured":"R.\u00a0FitzHugh, Biological Engineering, Inter-University Electronic Series\u00a09, ed. 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