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Attenuant cycles of population models with periodic carrying capacity. (English) Zbl 1067.92048
Summary: This paper considers attenuation of cycles generated by periodic difference equations for population dynamics. This study concerns the second conjecture of J. M. Cushing and S. M. Henson [ibid. 8, No. 12, 1119–1120 (2002; Zbl 1023.39013)], which was recently resolved affirmatively by S. Elaydi and R. J. Sacker [see J. Differ. Equations 208, 258–273 (2005; Zbl 1067.39003)]. We extend their result and obtain a sufficient condition for attenuation of cycles in population models. This sufficient condition is applicable to a wide class of periodic difference equations with arbitrary period. For an illustration, the result is applied to the Beverton-Holt equation and other specific population models.

MSC:
92D25 Population dynamics (general)
39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
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[1] DOI: 10.1016/0040-5809(86)90038-9 · Zbl 0599.92021 · doi:10.1016/0040-5809(86)90038-9
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