Levine, Daniel S. Bifurcating periodic solutions for a class of age-structured predator- prey systems. (English) Zbl 0542.92023 Bull. Math. Biol. 45, 901-915 (1983). The author uses bifurcation theory to provide sufficient conditions for the existence of periodic solutions corresponding to the steady states of predator-prey systems. The characteristic of the system is that predators prefer to eat very old and very young preys. Such a condition leads to a system of partial differential equations of McKendrick’s type and to an integrodifferential equation of Volterra type. Reviewer: G.Karakostas Cited in 8 Documents MSC: 92D25 Population dynamics (general) 35B10 Periodic solutions to PDEs 45J05 Integro-ordinary differential equations 35B32 Bifurcations in context of PDEs Keywords:McKendrick type equations; Volterra type equations; predator-prey systems PDFBibTeX XMLCite \textit{D. S. Levine}, Bull. Math. Biol. 45, 901--915 (1983; Zbl 0542.92023) Full Text: DOI References: [1] Cheatum, E. L. and C. W. Severinghaus. 1950. ”Variations in Fertility of White Tailed Deer Related to Range Conditions”. Transactions of the Fifteenth North American Wildlife Conference. [2] Cushing, J. M. 1977. ”Bifurcation of Periodic Solutions of Integrodifferential Systems with Applications to Time Delay Models in Population Dynamics”.SIAM J. appl. Math. 33, 640–654. · Zbl 0381.45008 [3] –, 1980. ”Model Stability and Instability in Age-structured Populations”.J. theor. Biol. 86, 709–730. [4] – 1982. ”Bifurcation of Periodic Solutions of Nonlinear Equations in Age-structured Population Dynamics”. In.Proceedings of the International Conference on Nonlinear Mathematics and Applications, Arlington, TX. New York: Academic Press. · Zbl 0515.92018 [5] Gurtin, M. E. and D. S. Levine. 1979. ”On Predator-Prey Interactions with Predation Dependent on Age of Prey”.Math. Biosci. 47, 207–219. · Zbl 0435.92023 [6] – and—-. 1982. ”On Populations that Cannibalize their Young”.SIAM J. appl. Math. 42, 94–108. · Zbl 0501.92021 [7] – and R. C. MacCamy. 1979. ”Some Simple Models for Non-linear Age-dependent Population Dynamics”.Math. Biosci. 43, 199–211. · Zbl 0397.92025 [8] Hassell, M. P. 1979.The Dynamics of Arthropod Predator-Prey Systems. Princeton, NJ: Princeton University Press. · Zbl 0429.92018 [9] Kolmogorov, A. N. 1936. ”Sulla Teoria di Volterra della Lotta per l’Esistenza”.Biorn. Inst. Intal. Attuari 7, 74–80. · JFM 62.1263.01 [10] Levine, D. S. 1981. ”On the Stability of a Predator-Prey System with Egg-eating Predators”.Math. Biosci. 56, 27–46. · Zbl 0461.92015 [11] McKendrick, A. G. 1926. ”Applications of Mathematics to Medical Problems”.Proc. Edinb. math. Soc. 44, 98–130. · JFM 52.0542.04 [12] Mech, L. D. 1970,The Wolf: Ecology and Behavior of an Endangered Species, Garden City, NY: Natural History Press. [13] Nicholson, A. J. 1954. ”An Outline of the Dynamics of Animal Populations”.Aust. J. Zool. 2, 9–65. [14] Ricklefs, R. E. 1973.Ecology, Newton, MA: Chiron Press. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.