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Models for pair formation in bisexual populations. (English) Zbl 0714.92018
Summary: Birth, death, pair formation, and separation are described by a system of three nonlinear homogeneous ordinary differential equations. The qualitative properties of the system are investigated, in particular the conditions for existence and global stability of the bisexual state.

MSC:
92D25 Population dynamics (general)
34C99 Qualitative theory for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
34D99 Stability theory for ordinary differential equations
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[1] Dietz, K., Hadeler, K. P.: Epidemiological models for sexually transmitted diseases. J. Math. Biol. 26, 1–25 (1988) · Zbl 0643.92015 · doi:10.1007/BF00280169
[2] Dowse, H. B., Ringo, J. M., Barton, K. M.: A model describing the kinetics of mating in Drosophila. J. Theor. Biol. 121, 173–183 (1986) · doi:10.1016/S0022-5193(86)80091-1
[3] Fredrickson, A. G.: A mathematical theory of age structure in sexual populations: Random mating and monogamous marriage models. Math. Biosci. 10, 117–143 (1971) · Zbl 0216.55002 · doi:10.1016/0025-5564(71)90054-X
[4] Hadeler, K. P., Glas, D.: Quasimonotone systems and convergence to equilibrium in a population genetic model. J. Math. Anal. Appl. 95, 297–303 (1983) · Zbl 0515.92012 · doi:10.1016/0022-247X(83)90108-7
[5] Hadeler, K. P., Waldstätter, R., Wörz-Busekros, A.: Models for pair formation. In: Conference Report, Deutsch-Französisches Treffen über Evolutionsgleichungen, Blaubeuren, 3.–9. Mai 1987, Semesterbericht Funktionalanalysis Tübingen 1987, pp. 31–40 · Zbl 0714.92018
[6] Hadeler, K. P.: Pair formation in age structured populations. In: Kurzhanshij, A., Sigmund, K. (eds.) Proceedings, Workshop on Selected Topics in Biomathematics, IIASA, Laxenburg, Austria 1987 · Zbl 0667.92013
[7] Hirsch, M. W.: Systems of differential equations which are competitive or cooperative I. Limit sets. SIAM J. Math. Anal. 13, 167–179 (1982) · Zbl 0494.34017 · doi:10.1137/0513013
[8] Hofbauer, J., Sigmund, K.: Evolutionstheorie und dynamische Systeme. Berlin Hamburg: Parey 1984 · Zbl 0578.92015
[9] Impagliazzo, J.: Deterministic aspects of mathematical demography. (Biomathematics, vol. 13) Berlin Heidelberg New York: Springer 1985
[10] Karlin, S., Lessard, S.: Theoretical studies on sex ratio evolution. (Monographs in population biology, vol. 22) Princeton: Princeton University Press 1986
[11] Kendall, D. G., Stochastic processes and population growth. Roy. Statist. Soc., Ser B 2, 230–264 (1949) · Zbl 0038.08803
[12] Keyfitz, N.: The mathematics of sex and marriage. Proceedings of the Sixth Berkeley Symposion on Mathematical Statistics and Probability. Vol. IV: Biology and health, pp. 89–108 (1972)
[13] McFarland, D. D., Comparison of alternative marriage models. In: Greville, T. N. T. (ed.) Population dynamics, pp. 89–106, New York London: Academic Press 1972
[14] Parlett, B.: Can there be a marriage function? In: Greville, T. N. T. (ed.) Population Dynamics pp. 107–135. New York London: Academic Press 1972
[15] Pollak, R. E.: The two-sex problem with persistent unions: a generalization of the birth matrix-mating rule model. Theor. Popul. Biol. 32, 176–187 (1987) · Zbl 0623.92022 · doi:10.1016/0040-5809(87)90046-3
[16] Pollard, J. H.: Mathematical models for the growth of human populations, Chap. 7: The two sex problem. Cambridge: Cambridge University Press 1973 · Zbl 0295.92013
[17] Staroverov, O. V.: Reproduction of the structure of the population and marriages. (Russian) Ekonomika i matematičeskije metody 13, 72–82 (1977)
[18] Wallace, B.: Mating kinetics in Drosophila. Behav. Sci. 30, 149–154 (1985) · doi:10.1002/bs.3830300305
[19] Wallace, B.: Kinetics of mating in Drosophila. I, D. melanogaster, an ebony strain, preprint. Dept. Biol., Virginia Polytechnic and State University
[20] Williams, G. C: Sex and evolution. Monographs in population biology, vol. 8. Princeton: Princeton University Press 1975
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