Abstract
A principle of the transfer of a number of local properties of nonautonomous models of competition to a nonlocal Poincare mapping is given. Based on the suggested “geometric” approach, criteria of the biological selection in a periodically varying medium are defined.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Vance, R.R. and Coddington, E.A., A Nonautonomous Model of Population Growth, J. Math. Biol., 1989, vol. 27, no. 5, pp. 491–506.
Gimel'farb, A.A., Ginzburg, L.R., Poluektov, R.A., et al., Dinamicheskaya teoriya biologicheskikh populyatsii (The Dynamic Theory of Biological Populations), Moscow: Nauka, 1974.
Arnol'd, V.I., Obyknovennye differentsial'nye uravneniya (Ordinary Differential Equations), Moscow: Nauka, 1984.
Il'ichev, V.G., Sign Structures of Matrices and Their Application to the Analysis of Dynamic Systems, Avtom. Telemekh., 1999, no. 10, pp. 89–100.
Opoitsev, V.I., Nelineinaya sistemostatika (Nonlinear Systems Statics), Moscow: Nauka, 1986.
Krasnosel'skii, M.A. and Zabreiko, P.P., Geometricheskie metody nelineinogo analiza (Geometric Methods of the Nonlinear Analysis), Moscow: Nauka, 1975.
Il'ichev, V.G., Delta Functions and the Theory of Biological Competition in a Variable Medium, Avtom. Telemekh., 1996, no. 11, pp. 115–127.
Il'ichev, V.G. and Il'icheva, O.A., Universal Constants of a Reserve and Criteria of Selection in a Periodically Varying Medium, Zh. Obshch. Biol., 2000, vol. 61, no. 6, pp. 565–582.
Il'ichev, V.G., Delta Functions and Investigation of Ecological Volterra Models in a Variable Medium, Izv. Vuzov. Mat., 1998, no. 4, pp. 23–33.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Il'ichev, V.G. Geometric Methods of the Investigation of Competition Models in a Periodic Medium. Automation and Remote Control 63, 613–626 (2002). https://doi.org/10.1023/A:1015130215571
Issue Date:
DOI: https://doi.org/10.1023/A:1015130215571