zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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:
92D25Population dynamics (general)
34C99Qualitative theory of solutions of ODE
34A34Nonlinear ODE and systems, general
34D99Stability theory of ODE
References:
[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
[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
[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
[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)
[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
[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