| 外部环境干扰下的非线性渔业资源种群动力模型及分析 |
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| 引用本文： | 顾恩国,范致鉴,梁艳,廖容云.外部环境干扰下的非线性渔业资源种群动力模型及分析[J].中南民族大学学报(自然科学版),2011,30(3):98-102,126. |
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| 作者姓名： | 顾恩国 范致鉴 梁艳 廖容云 |
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| 作者单位： | 中南民族大学数学与统计学学院,武汉,430074 |
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| 基金项目： | 国家自然科学基金资助项目(10871209); 中南民族大学自然科学基金资助项目(YZZ060277) |
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| 摘 要： | 运用欧拉方法获得离散的捕食者-食饵差分系统方程,并考虑添加一对捕食者的扰动项后建立了一外部环境干扰下的非线性渔业资源种群模型,从而定量分析正不动点的存在性、稳定性和局部分叉,发现系统可能产生Neimark分叉和倍周期分叉,用全局分析方法描述了资源在什么范围具有可持续性利用,即保持渔业资源种群数量不枯竭的资源储量范围.
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| 关 键 词： | 捕食者-食饵模型 欧拉方法 正平衡点的稳定性 倍周期分叉 Neimark分叉 可行域 |
Analysis of the Nonlinear Dynamical Model of Fishery Resource with An External Interference |
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| Gu Enguo,Fan Zhijian,Liang Yan,Liao Rongyun.Analysis of the Nonlinear Dynamical Model of Fishery Resource with An External Interference[J].Journal of South-Central Univ for,2011,30(3):98-102,126. |
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| Authors: | Gu Enguo Fan Zhijian Liang Yan Liao Rongyun |
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| Institution: | Gu Enguo,Fan Zhijian,Liang Yan,Liao Rongyun(College of Mathematics and Statistics,South-Central University for Nationalities,Wuhan 430074,China) |
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| Abstract: | In this paper,we use Euler method to obtain a two-dimensional difference system,establish the nonlinear fishery resource model in which predators are influenced by adding an external interference,and quantitatively study the existence,stability of positive equilibrium and local bifurcations.Then we find that both Neimark and flip bifurcations probably occur.Finally we show the extents of sustainable use of fishery resources,that is the exhausted conditions of resources,by the use of global analysis. |
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| Keywords: | prey-predator model Euler method stability of the positive equilibrium flip bifurcation Neimark bifurcation feasible domain |
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