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对"一类带收获率的离散时滞人口模型正周期解存在性"的探究

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对"一类带收获率的离散时滞人口模型正周期解存在性"的探究 廖华英, 徐向阳, 胡启宙南昌师范学院数学与计算机科学系, 南昌 330032 Exploration about the Existence of Positive Periodic Solutions for a Class of Discrete Time Delayed Population Model with Harvesting Rate LIAO Huaying, XU Xiangyang, HU YuzhouDepartment of Mathematics and Computer Science, Nanchang Normal University, Nanchang 330032
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摘要本文对一类带收获率的离散时滞人口模型正周期解的存在性进行了探究. 以迭合度理论中的延拓定理为理论基础， 通过分析变形、利用一些不等式估计技巧构造了两个有界开集， 再利用Brouwer度的同伦不变性，我们计算得知在这两个有界开集中算子的Brouwer度不等于零， 从而得到了这类离散模型两个正周期解存在的充分条件. 最后， 举出两个例子来验证我们的主要结论， 并提出了有待进一步解决的问题.
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收稿日期: 2015-09-11
PACS:O175.7
引用本文:
廖华英, 徐向阳, 胡启宙. 对"一类带收获率的离散时滞人口模型正周期解存在性"的探究[J]. 应用数学学报, 2016, 39(4): 598-609. LIAO Huaying, XU Xiangyang, HU Yuzhou. Exploration about the Existence of Positive Periodic Solutions for a Class of Discrete Time Delayed Population Model with Harvesting Rate. Acta Mathematicae Applicatae Sinica, 2016, 39(4): 598-609.
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[1]廖华英, 周正. 一类带收获项的离散Lotka-Volterra合作系统的四个正周期解[J]. 应用数学学报, 2016, 39(3): 441-451.



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