Asymptotic behavior of a delay differential model in population dynamics
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Considered a scalar nonlinear delay differential equation of the certain species, for which suf-ficient conditions for oscillation of all solutions and asymptotical stability of the positive equilibrium are obtained.
Delay differential equations, richard's nonlinearity, oscillation, stability
Короткий адрес: https://sciup.org/147155104
IDR: 147155104 | DOI: 10.14529/ctcr160214
Список литературы Asymptotic behavior of a delay differential model in population dynamics
- 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.
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