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A note on attenuant cycles of population models with periodic carrying capacity. (English) Zbl 1056.92046
Summary: We consider attenuant cycles of population models. This study concerns the second conjecture of J. M. Cushing and S. M. Henson [J. Difference Eq. Appl. 8, 1119-1120 (2002; Zbl 1023.39013)], which was recently resolved affirmatively by S. M. Elaydi and R. Sacker [Global stability of periodic orbits of nonautonomous difference equations in population biology and the Cushing-Henson conjectures. Proc. 8th Int. Conf. Diff. Eq., Brno (in press). They showed that the periodic fluctuations in the carrying capacity always reduce the average of population densities in the Beverton-Holt equation. We extend this result and give a class of population models in which the periodic fluctuations in the carrying capacity always reduce the average of population densities.

MSC:
92D25 Population dynamics (general)
39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
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