Asymptotic Behavior of a Delay Differential Model in Population Dynamics

L. Berezansky, L. Idels

Abstract


Considered a scalar nonlinear delay differential equation of the certain species, for which sufficient conditions for oscillation of all solutions and asymptotical stability of the positive equilibrium are obtained.

Keywords


Delay differential equations; Richard’s nonlinearity; Oscillation; Stability

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References


Brauer F., Castillo-Chavez C. Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, 2001.

Kot M. Elements of Mathematical Ecology, Cambridge Univ. Press, 2001.

Baker C.T.H. Retarded Differential Equations, J. Comp. Appl. Math., 2000, 125, pp. 309–335.

Hutchinson G.E. Circular Causal Systems in Ecology, Ann. N.Y. Acad. Sci., 50, pp. 221–246.

Zhang B.G., Gopalsamy K. Oscillation and Nonoscillation in a Nonautonomous Delay-Logistic Equation, Quart. Appl. Math., 1988, XLVI, pp. 267–273.

Gyori I., Ladas G. Oscillation Theory of Delay Differential Equations, 1991, Clarendon Press, Oxford.

Gopalsamy K. Stability and Oscillation in Delay Differential Equations of Population Dynamics, 1992, Kluwer Academic Publishers, Dordrecht, Boston, London.

Erbe L.N., Kong Q., Zhang B.G. Oscillation Theory for Functional Differential Equations, 1995, Marcel Dekker, New York, Basel.

Tsoularis A., Wallace J. Analysis of Logistic Growth Models. Mathematical Biosciences, 2002, 179, pp. 21–55.

Pella J., Tomlinson P. A Generalized Stock-Production Model. Inter.-Am. Trop. Tuna Comm. Bull., 1969, 13, pp. 421–496.

Miguel Jose J., Ponosov A., Shindiapin A. On a Delay Equation with Richards’ Nonlinearity. Proceedings of the Third World Congress of Nonlinear Analysts, Part 6 (Catania, 2000). Nonlinear Anal., 2001, 47, no. 6, pp. 3919–3924.

Krisztin T. On Stability Properties for One-Dimensional Functional-Differential Equations. Funkcial. Ekvac., 1991, 34, no. 2, pp. 241–256.

Bellman R., Cooke K. Differential-Difference Equations. Academic Press, New York – London 1963. 462 p.

Kolmanovskii V., Myshkis A., Introduction to the Theory and Applications of Functional-Differential Equations. Mathematics and Its Applications, 463. Kluwer Academic Publishers, Dordrecht, 1999. 648 p.




DOI: http://dx.doi.org/10.14529/ctcr160214

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