Geodesic
A phenomenological approach to non equilibrium self-cooperative relaxation processes: Liquori-Tripiciano versus Verhulst cell growth equation
Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 83 (1989) no. 1, pp. 307-311 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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An analytic function shown by Liquori and Tripiciano to be suitable to explain sigmoidal growth curves is compared with the classical logistic equation of Verhulst. It is shown that Liquori-Tripiciano function displays a higher flexibility and offers operational advantages with respect to Verhulst logistic equation. Furthermore at variance with the latter equation it allows to study the effect of temperature on growth curves. For highly cooperative growth processes, the two sigmoidal curves calculated according to Liquori-Tripiciano equation and Verhulst equation virtually coincide. 
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     author = {Liquori, Alfonso M. and Lavenda, Bernard and Florio, Arnaldo},
     title = {A phenomenological approach to non equilibrium self-cooperative relaxation processes: {Liquori-Tripiciano} versus {Verhulst} cell growth equation},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali},
     pages = {307--311},
     year = {1989},
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Liquori, Alfonso M.; Lavenda, Bernard; Florio, Arnaldo. A phenomenological approach to non equilibrium self-cooperative relaxation processes: Liquori-Tripiciano versus Verhulst cell growth equation. Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 83 (1989) no. 1, pp. 307-311. http://geodesic.mathdoc.fr/item/RLINA_1989_8_83_1_a43/

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[2] Liquori A.M. and Florio A., 1984. Influence of Temperature on the Rate of Cell Growth: A Quantitative Approach Based on Non Equilibrium Thermodynamics. Rend. Acc. Naz. Lincei, 76: 382-387. | fulltext EuDML

[3] Prigogine I., 1962. Introduzione alla termodinamica dei processi irreversibili. A cura e con prefazione di A.M. Liquori, Leonardo Editore, Roma, 1971.

[4] Monod J., 1958. Recherches sur la croissance des cultures bactériennes. Hermann, Paris.

[5] Liquori A.M., Monroy A., Parisi E. and Tripiciano A., 1981. A Theoretical Equation for Diauxic Growth and Its Applications to the Kinetics of the Early Development of the Sea Urchin Embryo. Differentiation, 20: 174-175.

[6] Verhulst P.F., 1838. Corr. Math. Phys., 10: 113.

[1] J. Chela Flores, A.M. Liquori and A. Florio. A kinetic thermodynamic phenomenological approach to genetic expression of heat-shock proteins. J. Theor. Biol., 1988, 134, 319-325.

[2] A.M. Liquori and S. Giove. The temporal evolution of AIDS manifestation in a group of HIV virus infected individuals. J. Theor. Biol., 1989, 140, 571-574.