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Biological Cybernetics

, Volume 42, Issue 3, pp 221–229 | Cite as

On Gompertz growth model and related difference equations

  • A. G. Nobile
  • L. M. Ricciardi
  • L. Sacerdote
Article
  • 365 Downloads

Abstract

Within the context of the dynamics of populations described by first order difference equations a datailed study of the Gompertz growth model is performed. This is mainly achieved by proving several theorems for a class of difference equations generalizing the Gompertz equation. Some interesting features of the discrete Gompertz model, not exhibited by other well known growth models, are finally pointed out.

Keywords

Related Difference Growth Model Difference Equation Order Difference Gompertz Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Capocelli, R.M., Ricciardi, L.M.: Growth with regulation in random environment. Kybernetik 15, 147–157 (1974)Google Scholar
  2. Capocelli, R.M., Ricciardi, L.M.: A note on growth processes in random environment. Biol. Cybern. 18, 105–109 (1975)Google Scholar
  3. Feller, W.: On the logistic law of growth and its empirical verifications in biology. Acta Biotheor. 5, 51–66 (1939)Google Scholar
  4. Levy, G., Lessman, F.: Finite difference equations. New York: The Macmillan Company (1961)Google Scholar
  5. Li, T.Y., York, J.A.: Period three implies chaos. Ann. Math. 82, 985–992 (1975)Google Scholar
  6. May, R.M.: Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos. Science 186, 645–647 (1974)Google Scholar
  7. May, R.M.: Biological populations obeying difference equations: stable points, stable cycles, and chaos. J. Theor. Biol. 49, 511–524 (1975)Google Scholar
  8. May, R.M.: Simple mathematical models with very complicated dynamics. Nature 261, 459–467 (1976)Google Scholar
  9. May, R.M.: Bifuccations and dynamics complexity in ecological systems. Ann. N.Y. Acad. Sci. 316, 517–529 (1979)Google Scholar
  10. May, R.M., Oster, F.G.: Bifurcations and dynamics complexity in simple ecological models. Am. Nat. 110, 573–599 (1976)Google Scholar
  11. Nobile, A.G., Ricciardi, L.M.: Growth and extinction in random environment. In: Applications of information and control systems. Lainiotis, D.G., Tzannes, N.S. (eds.) pp. 455–465. Dordrecht: D. Reidel Publ. Co. 1980Google Scholar
  12. Ricciardi, L.M.: Diffusion processes and related topics in biology. Berlin, Heidelberg, New York: Springer 1977Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • A. G. Nobile
    • 1
  • L. M. Ricciardi
    • 1
    • 2
  • L. Sacerdote
    • 1
  1. 1.Instituto di Science dell'InformazioneUniversità di SalernoSalernoItaly
  2. 2.Istituto di MatematicaUniversità degli StudiNapoliItaly

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