Abstract
We discuss the long-time behavior of Andreoli's differential equation for genetic algebras and for Bernstein algebras and show convergence to an equilibrium in both cases. For a class of Bernstein algebras this equilibrium is determined explicitly.
Similar content being viewed by others
References
Andreoli, G.: Algebre non associative e sistemi differenziati di Riccati in un problema di Genetica. Ann. Mat. Pura Appl. 49, 97–116 (1960)
Gonshor, H.: Special train algebras arising in genetics. Proc. Edinb. Math. Soc., II. Ser. 12, 41–53 (1960)
Grishkov, A. N.: On the genetic property of Bernstein algebras. Sov. Math. Dokl. 35 (1987) 489–492 (No. 3)
Hentzel, I. R., Peresi, L. A.: Semi-prime Bernstein algebras. Arch. Math. 52, 539–543 (1989)
Heuch, L: Genetic algebras and time continuous models. Theor. Popul. Biol. 4, 133–144 (1973)
Holgate, P.: Genetic algebras satisfying Bernstein's principle. J. Lond. Math. Soc., II. Ser. 9, 613–623 (1975)
Walcher, S.: On Bernstein algebras which are train algebras. Proc. Edinb. Math. Soc. 35, 159–166 (1992)
Walcher, S.: Bernstein algebras which are Jordan algebras. Arch. Math. 50, 218–222 (1988)
Wörz-Busekros, A.: Algebras in Genetics. (Lect. Notes Biomath., vol. 36) Berlin Heidelberg New York: Springer 1980
Wörz-Busekros, A.: Bernstein algebras. Arch. Math. 48, 388–398 (1987)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gradl, H., Walcher, S. On continuous time models in genetic and Bernstein algebras. J. Math. Biol. 31, 107–113 (1992). https://doi.org/10.1007/BF00163845
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00163845