| 服从Gompertz增长的两斑块种群模型及其定性分析 |
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| 引用本文： | 尤 亮,张瑞明,冯晓龙.服从Gompertz增长的两斑块种群模型及其定性分析[J].西北农业学报,2013,22(9):198-202. |
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| 作者姓名： | 尤 亮 张瑞明 冯晓龙 |
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| 作者单位： | （西北农林科技大学 理学院 应用数学研究所，陕西杨凌 712100） |
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| 基金项目： | 西北农林科技大学引进人才科研启动费（Z11021105）。 |
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| 摘 要： | 为研究同一个种群分布在保护区和非保护区两个不同的斑块环境中的生长情况，建立种群密度服从Gompertz增长的生物模型。分别应用微分方程理论和数学软件对模型进行定性分析和数值分析，得到模型有唯一的稳定的正规结点。即两个斑块内的种群密度随着时间的增长，最终会稳定在一个固定值。同时讨论斑块间不存在迁移和努力度逐渐增大时的两斑块内种群的密度情况。结果表明：若不存在斑块间的迁移，保护区斑块内种群密度将会达到最大环境容量，而非保护区斑块内种群密度将趋于稳定；随着努力度的增加，会出现过度捕捞，最终导致非保护区斑块内的种群趋于灭亡。
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| 关 键 词： | 两斑块 Gompertz增长 定性分析 数值分析 |
Population Model of Two Patches with Gompertz Law of Growth and Its Qualitative Analysis |
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| YOU Liang,ZHANG Ruiming and FENG Xiaolong.Population Model of Two Patches with Gompertz Law of Growth and Its Qualitative Analysis[J].Acta Agriculturae Boreali-occidentalis Sinica,2013,22(9):198-202. |
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| Authors: | YOU Liang ZHANG Ruiming and FENG Xiaolong |
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| Abstract: | In order to study the growth of a population distributes in two different patches,we establish a biological model of population density which obeys Gompertz growth. Differential equation theory and mathematical software are used respectively to conduct qualitative analysis and numerical analysis for the model, and we obtain an unique regular stable node of the model. Thus we draw a conclusion that the population density within the two patches will eventually be stabilized at a fixed value with time growing. Meanwhile, the density of the population is considered in two cases: when there is no migration between the two patches and when the effortsgradually increase.The population density within the protected areas will reach maximum environmental capacity while that of non protected areas will stabilize;there will be overfishing with the increase of effort level, which eventually leads the population within the non protected to tend to extinct. |
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| Keywords: | Two patches Gompertz law Qualitative analysis Numerical analysis |
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