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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.
39A11Stability of difference equations (MSC2000)
39A20Generalized difference equations
92D25Population dynamics (general)