an:02109979
Zbl 1056.92046
Kon, Ryusuke
A note on attenuant cycles of population models with periodic carrying capacity
EN
J. Difference Equ. Appl. 10, No. 8, 791-793 (2004).
00107961
2004
j
92D25 39A11 39A10
periodic difference equations; average population densities; concave functions; periodic fluctuations
Summary: We consider attenuant cycles of population models. This study concerns the second conjecture of \textit{J. M. Cushing} and \textit{S. M. Henson} [J. Difference Eq. Appl. 8, 1119-1120 (2002; Zbl 1023.39013)], which was recently resolved affirmatively by \textit{S. M. Elaydi} and \textit{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.
Zbl 1023.39013