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Zbl 1149.39300
Stević, Stevo
A short proof of the Cushing-Henson conjecture. (English)
[J] Discrete Dyn. Nat. Soc. 2006, Article ID 37264, 5 p. (2006). ISSN 1026-0226; ISSN 1607-887X/e

Summary: We give a short proof of the Cushing-Henson conjecture [cf. {\it J. M. Cushing} and {\it S. M. Henson}, J. Difference Equ. Appl. 8, No. 12, 1119--1120 (2002; Zbl 1023.39013)] concerning the Beverton-Holt difference equation [cf. {\it R. J. Beverton} and {\it S. J. Holt}, On the dynamics of exploited fish populations. Fish. Invest. 19, HM50, London (1957)] which is important in theoretical ecology. The main result shows that a periodic environment is always deleterious for populations modeled by the Beverton-Holt difference equation.

MSC 2000:: *39A11 Stability of difference equations
39A20 Generalized difference equations
92D25 Population dynamics
92D40 Ecology

Keywords: positive solution; rational difference equation; Cushing-Henson conjecture; Beverton-Holt difference equation; ecology; population

Citations: Zbl 1023.39013

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