Geodesic
On oscillation of solutions for some nonlinear equations of population dynamics
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 124, pp. 696-706

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Several nonlinear equations being models of population dynamics and hematopoiesis are considered in this paper. For these equations conditions of oscillation for solutions about nontrivial equilibrium position are obtained.
Keywords: functional differential equations, Hutchinson’s equation, Nicholson’s blowflies equation, concentrated delay, distributed delay.
Mots-clés : Lasota-Wazewska equation 
T. L. Sabatulina. On oscillation of solutions for some nonlinear equations of population dynamics. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 124, pp. 696-706. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_124_a13/
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[1] L. Berezansky, E. Braverman, “Linearized oscillation theory for a nonlinear equation with a distributed delay”, Mathematical and Computer Modelling, 48 (2008), 287–304

[2] S. A. Gusarenko, A. I. Domoshnitskiy, “About asymptotic and oscillation characteristics of first-order linear scalar functional differential equations”, Differential Equations, 25:12 (1989), 2090–2103 (In Russian)

[3] I. Györi, G. Ladas, Oscillation theory of delay differential equations: with applications, Oxford University Press, New York, 1991, 368 pp.

[4] A. D. Myshkis, “On solutions of linear homogeneous differential equations of the first order of stable type with a retarded argument”, Sbornik: Mathematics, 28(70):3 (1951), 641–658 (In Russian)

[5] R. G. Koplatadze, T. A. Chanturiya, “About oscillating and monotone solutions of differential first-order equation with retarded argument”, Differential Equations, 18:8 (1982), 1463–1465 (In Russian)

[6] T. L. Sabatulina, “On oscillating and sign-definite solutions to autonomous functional-differential equations”, J. Math. Sci., 230:5 (2018), 766–769

[7] T. L. Sabatulina, “On oscillating and sign-definite solutions to autonomous functional-differential equations”, J. Math. Sci., 230:5 (2018), 766–769

[8] V. V. Malygina, T. L. Sabatulina, “Sign-definiteness of solutions and stability of linear differential equations with variable distributed delay”, Russian Mathematics, 2008, no. 8, 73–77 (In Russian)

[9] G. E. Hutchinson, “Circular causal in ecology”, Ann. N. Y. Acad. Sci, 50 (1948), 221–246

[10] M. Wazewska-Czyzewska, A. Lasota, “Mathematical problems of dynamics of red blood cells production (Polish)”, Mat. Stos, 3:6 (1976), 23–40

[11] A. J. Nicholson, “Compensatory reactions of populations to stresses, and their evolutionary significance”, Austral. J. Zool, 1954, no. 2, 1–8

[12] A. Nicholson, “An outline of the dynamics of animal populations”, Austral. J. Zool, 1954, no. 2, 9–65

[13] R. M. May (ed.), “Models for single populations”, Theoretical Ecology: Principles and Applications, Blackwell Scientific, Oxford, 1976, 4–25

[14] W.S. C. Gurney, S. P. Blythe, R. M. Nisbet, “Nicholson's blowflies revisited”, Nature, 1980, no. 287, 17–21