zbMATH — the first resource for mathematics

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.

92D25 Population dynamics (general)
39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
Full Text: DOI
[1] DOI: 10.1016/0040-5809(86)90038-9 · Zbl 0599.92021 · doi:10.1016/0040-5809(86)90038-9
[2] DOI: 10.1080/10236190108808308 · Zbl 1002.39003 · doi:10.1080/10236190108808308
[3] DOI: 10.1080/1023619021000053980 · Zbl 1023.39013 · doi:10.1080/1023619021000053980
[4] Elaydi, S. and Sacker, R.J., Global stability of periodic orbits of non-autonomous difference equations and population biology,Journal of Differential Equations(in press). · Zbl 1067.39003
[5] Elaydi, S. and Sacker, R.J., Global stability of periodic orbits of nonautonomous difference equations in population biology and the Cushing-Henson conjectures,Proceedings of the 8th International Conference on Difference Equations and Applications, Brno, Czech Republic (in press). · Zbl 1087.39504
[6] DOI: 10.1080/10236199908808169 · Zbl 0988.39011 · doi:10.1080/10236199908808169
[7] DOI: 10.1007/BF00276199 · Zbl 0638.92019 · doi:10.1007/BF00276199
[8] DOI: 10.1007/s00285-003-0224-8 · Zbl 1050.92045 · doi:10.1007/s00285-003-0224-8
[9] DOI: 10.1086/283092 · doi:10.1086/283092
[10] DOI: 10.1016/S0893-9659(03)80027-7 · Zbl 1049.39017 · doi:10.1016/S0893-9659(03)80027-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.