Hypergraphic Functions and Bifurcations in Recurrence Relations

In this paper, bifurcations of the recurrence relation Xn + 1 = F(Xn) are studied. For a certain class of functions F, it is proved that when any cycle bifurcates, it produces a nearby one of double the period. The class of functions is defined by a differential inequality which is satisfied by seve...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 1978-06, Vol.34 (4), p.687-691
Main Author: Allwright, D. J.
Format: Article
Language:English
Subjects:
Fixed point property
Mathematical functions
Recurrence relations
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Summary:In this paper, bifurcations of the recurrence relation Xn + 1 = F(Xn) are studied. For a certain class of functions F, it is proved that when any cycle bifurcates, it produces a nearby one of double the period. The class of functions is defined by a differential inequality which is satisfied by several functions that have been used in models of biological populations.
ISSN:0036-1399
1095-712X
DOI:10.1137/0134057