有保护区的海洋渔业资源离散动力学模型分析  

Analysis of Discrete Dynamical Model for a Marine Fishery with a Protected Fishing Zone

作　　者：顾恩国[1] 李远平[1] 

机构地区：[1]中南民族大学数学与统计学学院,湖北武汉430074

出　　处：《应用数学》2012年第3期685-690,共6页Mathematica Applicata

基　　金：国家自然科学基金资助项目(10871209)

摘　　要：假设海洋渔业资源分属于保护区和非保护区两个区域,本文建立一个渔业资源储量-捕捞力度模型,用聚合方法得到一个简化的离散动力系统,从而分析正不动点的存在性、稳定性以及关于保护区面积比例的局部分叉,运用中心流形定理分析平衡点的局部稳定性,并用数值模拟验证不动点的局部分叉.最后,用全局分析方法分析保护区面积比例变化对可行吸引域的结构和大小的影响,从而揭示保护区对渔业资源可持续利用的影响.In this paper, the marine fishery resources are supposed to be subdivided into two zones, a reserve area and a fishing area, then a stock-effort dynamical model is estab- lished. The dynamical system is reduced by aggregated methods, and qualitative methods are used to analyze the existence of positive fixed points, stability and local bifurcations about the proportion of marine areas protected, Center-Manifold theorem is used to analyze the local stability of fixed points, and numerical simulation is used to verify the local bifurcations of fixed points. Finally the global method is used to analyze the influence of the protected area proportion on the feasible domain,and the results reveal how much reserve area is beneficial to the sustainable use of the fishery resource.

关 键 词：渔业资源储量-捕捞力度模型 聚合方法 中心流形定理 正平衡点的稳定性 Neimark分叉 可行吸引域 

分 类 号：O19[理学—数学]