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Periodic solutions of population models in a periodically fluctuating environment. (English) Zbl 0746.92022
Summary: A periodically fluctuating environment is assumed in a population- modeling process that generates nonautonomous difference equations. The existence and uniqueness of periodic solutions are studied. A sufficient condition for existence and a necessary condition for uniqueness are obtained. Stability of the periodic solutions is investigated. Several numerical examples are given to illustrate the basic results, and a brief discussion is presented.

92D40 Ecology
39A10 Additive difference equations
39A11 Stability of difference equations (MSC2000)
Full Text: DOI
[1] Clark, M.E.; Gross, L.J., Periodic solutions to nonautonomous difference equations, Math. biosci., 102, 105-119, (1991) · Zbl 0712.39014
[2] Feigenbaum, M.J., Universal behavior in nonlinear systems, Los alamos sci., 1, 4-27, (1980)
[3] Guckenheimer, J.; Oster, G.; Ipaktchi, A., The dynamics of density dependent population models, Math. biosci., 43, 101-147, (1977) · Zbl 0379.92016
[4] Hallam, T.G., Population dynamics in a homogeneous environment, (), 61-94
[5] Hallam, T.G.; Levin, S.A., ()
[6] Harper, J.L., The regulation of numbers and mass in plant populations, ()
[7] Kot, M.; Schaffer, W.M., The effects of seasonality on discrete models of population growth, Theor. popul. biol., 26, 340-360, (1984) · Zbl 0551.92014
[8] Li, J., Persistence in discrete age-structured population models, Bull. math. biol., 50, 351-366, (1988) · Zbl 0659.92019
[9] Li, J.; Hallam, T.G.; Ma, Z., Demographic variation and survival in discrete population models, IMA J. math. appl. med. biol., 4, 237-246, (1987) · Zbl 0629.92013
[10] May, R.M., Theoretical ecology: principles and applications, (1976), Saunders Philadelphia · Zbl 1228.92076
[11] May, R.M., Simple mathematical models with very complicated dynamics, Nature, 261, 459-467, (1976) · Zbl 1369.37088
[12] May, R.M.; Conway, G.R.; Hassell, M.P.; Southwood, T.R.E., Time delays, density-dependence, and single-species oscillations, J. anim. ecol., 43, 747-770, (1974)
[13] May, R.M.; Oster, G.F., Bifurcations and dynamic complexity in simple ecological models, Amer. nat., 110, 573-599, (1976)
[14] Smith, J.Maynard, Mathematical ideas in biology, (1968), Cambridge Univ. Press New York
[15] Nicholson, A.J.; Bailey, V.A., The balance of animal populations, part I, Proc. zool. soc. lond., 3, 551-598, (1935)
[16] Pianka, E.R., Ecology of the agamid lizard amphibolurus ilolepsis in western Australia, Copeia, 1971, 527-536, (1971)
[17] Pielou, E.C., Mathematical ecology, (1977), Wiley-Interscience New York · Zbl 0259.92001
[18] Pielou, E.C., Population and community ecology: principles and methods, (1978), Gordon and Breach New York · Zbl 0349.92024
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