| 摘要: |
| 本文提出了具有密度依赖出生率的非选择性半封闭捕获离散偏害模型.运用差分方程的迭代方法和比较原理,得出了系统持久性及灭绝性的一系列条件.通过构造适当的Lyapunov函数,得到一个系统全局吸引的充分条件.本研究结果表明,通过控制种群中可用于捕获的种群比例m(这与密度依赖的出生率有很大关系,系统可能是持久的、灭绝的、全局吸引的,或者一个种群持久而另一个灭绝,系统的动态行为变得复杂。通过数值模拟验证了主要结果的可行性. |
| 关键词: 密度依赖性出生率 偏害模型 持久性 灭绝性 非选择性捕获 |
| DOI：10.3969/J.ISSN.1000-5137.2024.03.001 |
| 分类号:O175.14 |
| 基金项目:The Scientific Research Project of Ningde Normal University(2021Q202,2022ZX415),the Natural Science Foundation of Fujian Province (2021J011155,FJ2021B031). |
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| Dynamic behavior of the discrete amensalism model with density dependent birth rate and nonselective harvesting in partial closure |
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XU Lili, LEI Chaoquan, XUE Yalong
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College of Mathematics and Physics, Ningde Normal University, Ningde 352000, Fujian, China
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| Abstract: |
| Discrete amensalism model with density dependent birth rate and nonselective harvesting in partial closure is proposed in this paper. Using the iteration scheme and the comparison principle of difference equations, a set of necessary criteria for the system’s permanence and extinction is established. By constructing a suitable Lyapunov function, a sufficient condition is obtained to ensure the global attractivity of the system. Our research demonstrates that by controling the portion of the stock that is available for harvesting m, which is quite related with density dependent birth rate, the system may be permanence, extinction, global attractivity, or one is permanent while the other will be driven to extinction, the dynamic behaviors of the system become complicated. The validity of the main results is illustrated by numerical simulations. |
| Key words: density dependent birth rate amensalism model permanence extinction nonselective harvesting |
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