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| Abstract: |
| Fractional linear maps have played a key role in mathematical biology, population dynamics, and other research areas. In this paper, a special kind of Ricatti map is studied in detail in order to determine the asymptotical behaviors of fixed points and periodic solutions. Making use of composition operation of maps and the methods of dynamical systems and qualitative theory, fixed points or periodic orbits are expressed precisely, average value of periodic solution is estimated concretely, and several different bounds are obtained for periodic solutions of the Beverton-Holt map when both intrinsic growth rate and carrying capacity change periodically. In addition, some sufficient conditions are given about the attenuation of periodic solution of the non-autonomous Beverton-Holt equation. Compared with present works in literature, our results about bounds of periodic solutions are more precise, and our proofs about the attenuation of periodic solution are more concise. |
| Key words: Beverton-Holt equation Cushing-Henson conjecture attenuation p-cycle |
| DOI：10.11916/j.issn.1005-9113.21030 |
| Clc Number:O175.7 |
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| Descriptions in Chinese: |
| Beverton-Holt方程的周期解性质研究 郝颖超, 李翠萍 （北京航空航天大学 数学科学学院，北京 100083） 中文说明：本文对一类特殊的Ricatti映射进行了详细研究.针对内禀增长率与环境容纳量均周期改变的Beverton-Holt映射的周期解给出了不同的界的估计,并给出了非自治Beverton-Holt方程周期解发生衰减的条件及新的证明. 关键词：Beverton-Holt方程，Cushing-Henson猜想，衰减，p-环 |
