Yang Zhichun, Huang Chuangxia, Zou Xingfu
College of Mathematical Sciences, Chongqing Normal University, Chongqing, 400047, People's Republic of China.
College of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, 410114, Hunan, People's Republic of China.
J Math Biol. 2018 May;76(6):1387-1419. doi: 10.1007/s00285-017-1172-z. Epub 2017 Sep 9.
In this paper, a very general model of impulsive delay differential equations in n-patches is rigorously derived to describe the impulsive control of population of a single species over n-patches. The model allows an age structure consisting of immatures and matures, and also considers mobility and culling of both matures and immatures. Conditions are obtained for extinction and persistence of the model system under three special scenarios: (1) without impulsive control; (2) with impulsive culling of the immatures only; and (3) with impulsive culling of the matures only, respectively. In the case of persistence, the persistence level is also estimated for the systems in the case of identical n patches, by relating the issue to the dynamics of multi-dimensional maps. Two illustrative examples and their numerical simulations are given to show the effectiveness of the results. Based on the theoretical results, some strategies of impulsive culling are provided to eradicate the population of a pest species.
本文严格推导了一个非常通用的n斑块脉冲延迟微分方程模型，用于描述单物种种群在n个斑块上的脉冲控制。该模型允许存在由未成熟个体和成熟个体组成的年龄结构，同时考虑了成熟个体和未成熟个体的迁移及捕杀情况。分别在三种特殊情形下得到了模型系统灭绝和持续存在的条件：（1）无脉冲控制；（2）仅对未成熟个体进行脉冲捕杀；（3）仅对成熟个体进行脉冲捕杀。在持续存在的情况下，通过将问题与多维映射的动力学联系起来，还对相同n个斑块情形下系统的持续水平进行了估计。给出了两个说明性例子及其数值模拟，以展示结果的有效性。基于理论结果，提供了一些脉冲捕杀策略以根除害虫物种的种群。
