Geodesic
Properties of solutions of a class of equations with lag which describe the dynamics of change in the population of a species with the age structure taken into account
Sbornik. Mathematics, Tome 45 (1983) no. 1, pp. 91-100 
Yu. S. Kolesov. Properties of solutions of a class of equations with lag which describe the dynamics of change in the population of a species with the age structure taken into account. Sbornik. Mathematics, Tome 45 (1983) no. 1, pp. 91-100. http://geodesic.mathdoc.fr/item/SM_1983_45_1_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The equation $$ \dot N=r\biggl[1-\dfrac{1}{K}\int_{h_1}^{h_2}H(s)N(t-s)\,ds\biggr]N, $$ generalizing the well-known Hutchinson equation, is used to describe the dynamics of change in the population of a species, with the age structure taken into account. Conditions are found for bifurcation of a periodic solution of this equation. The results obtained here are applied to explain some natural phenomena. Bibliography: 12 titles.

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

[2] May R. M., Stability and complexity in model ecosystems, Princeton University Press, Princeton, 1973

[3] Kolesov Yu. S., “Rezonansy v ekologii”, Issledovaniya po ustoichivosti i teorii kolebanii, 26–42, Yaroslavl, 1978 | Zbl

[4] Kolesov Yu. S., “Matematicheskie modeli ekologii”, Issledovaniya po ustoichivosti i teorii kolebanii, Yaroslavl, 1979, 3–40 | MR | Zbl

[5] Kolesov Yu. S., Shvitra D. I., Avtokolebaniya v sistemakh s zapazdyvaniem, Mokslas, Vilnyus, 1979 | MR | Zbl

[6] Lek D., Chislennost zhivotnykh i ee regulyatsiya v prirode, IL, M., 1957

[7] Kolesov Yu. S., “Garmonicheskie avtokolebaniya differentsialnykh uravnenii $n$-go poryadka s posledeistviem”, Vestn. Yarosl. un-ta, 1974, no. 7, 3–88 | MR

[8] Zakharov A. A., Kolesov Yu. S., Spokoinov A. N., Fedotov B. N., “Teoreticheskoe ob'yasnenie desyatiletnego tsikla kolebanii chislennosti mlekopitayuschikh v Kanade i Yakutii”, Issledovaniya po ustoichivosti i teorii kolebanii, Yaroslavl, 1980, 82–131

[9] Tavrovskii V. A. i dr., Mlekopitayuschie Yakutii, Nauka, M., 1971

[10] Hadeler K. P., “On the stability of the stationary state of a population growth equation with time lag”, J. Math. Biology, 3 (1976), 197–201 | DOI | MR | Zbl

[11] Walther H. O., “On a transcendental equation in the stability analysis of a population growth model”, J. Math. Biology, 3 (1976), 187–195 | DOI | MR | Zbl

[12] Nussbaum R. D., “Differential-delay equations with two time lags”, Mem. Amer. Math. Soc., 1978, no. 205, 1–62 | MR