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A short proof of the Cushing-Henson conjecture. (English) Zbl 1149.39300

Summary: We give a short proof of the Cushing-Henson conjecture [cf. J. M. Cushing and S. M. Henson, J. Difference Equ. Appl. 8, No. 12, 1119–1120 (2002; Zbl 1023.39013)] concerning the Beverton-Holt difference equation [cf. R. J. Beverton and 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:

39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations
92D25 Population dynamics (general)
92D40 Ecology

Citations:

Zbl 1023.39013
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References:

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[2] R. J. Beverton and S. J. Holt, On the Dynamics of Exploited Fish Populations, vol. 19 of Fish. Invest., HMSO, London, 1957.
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