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solutions of period three for a non-linear difference equation

Published online by Cambridge University Press:  17 February 2009

A. Brown
A. Brown
Affiliation:
Department of Theoretical Physics, Research School of Physical Sciences, Australian National University, G.P.O. Box 4, Canberra, A.C.T. 2601.
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Abstract

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The paper uses the factorisation method to discuss solutions of period three for the difference equation

which has been proposed as a simple mathematical model for the effect of frequency dependent selection in genetics. Numerical values are obtained for the critical values of a at which solutions of period three first appear. In addition, the interval in which stable solutions are possible has been determined. Exact solutions are given for the case a = 4 and these have been used to check the results.

Type
Research Article
Information
The ANZIAM Journal , Volume 25 , Issue 4 , April 1984 , pp. 451 - 462
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Brown, A., “Equations for periodic solutions of a logistic difference equation”, J. Austral. Math. Soc. Ser. B 23 (1981), 78–94.CrossRefGoogle Scholar
[2]Brown, A., “Solutions of period seven for a logistic difference equation”, Bull. Austral. Math. Soc. 26 (1982), 263–284.Google Scholar
[3]Clarke, B. C., “Frequency-dependent and density-dependent natural selection”, in The role of natural selection in human evolution (ed. Salzano, F. M.), (North-Holland, Amsterdam, 1975), 187–200.Google Scholar
[4]Clarke, B. C., “The evolution of genetic diversity”, Proc. Roy. Soc. London Ser. B 205 (1979), 453–474.Google Scholar
[5]Falconer, D. S., Introduction to quantitative genetics (Longman, London, 2nd edition, 1981), 43.Google Scholar
[6]Frauenthal, J. C., Introduction to population modeling (Birkhäuser, Basel, 1980), 71–73.Google Scholar
[7]Lewontin, R. C., The genetic basis of evolutionary change (Columbia Univ. Press, New York, 1974), 256–260.Google Scholar
[8]May, R. M., “Bifurcations and dynamic complexity in ecological systems”, Ann. N. Y. Acad. Sci. 316 (1979), 517–529.Google Scholar
[9]May, R. M., “Non-linear problems in ecology and resource management”, Lecture notes for Les Houches Summer School on “Chaotic Behaviour of Deterministic Systems”, July 1981.Google Scholar
[10]Parkin, D. T., An introduction to evolutionary genetics (Arnold, London, 1979), 81, 99–110.Google Scholar