具有跨区域的渔业资源的离散动力学模型分析  

Analysis of discrete dynamical model for transboundary fishing resources

作　　者：梁艳[1] 顾恩国[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：《湖北大学学报（自然科学版）》2012年第1期9-13,共5页Journal of Hubei University：Natural Science

基　　金：国家自然科学基金项目(10871209)资助

摘　　要：假设渔洋渔业资源分属于3个区域,每个区域各有一个船队进行捕获,利用两个时间刻度的存在性,鱼在3个区域内的游动比资源增长速度快,渔船的移动速度比船只数目变化快.在快的时间刻度下,全部渔业资源和船只的数目保持不变,在此条件下构造的一个渔业资源储量-捕捞力度离散动力学模型,用聚合方法得到一个简化的动力系统,从而定量分析正不动点的存在性、稳定性和局部分叉.最后,用全局分析方法来描述资源在什么范围可持续利用.It supposed that fishery resources were subdivided into three zones,and every zone harvested by a fleet.We took advantage of the existence of two time scales,this was,the migration of the fish among three fishing zones was assumed to be faster than the growth of the harvested stock.The displacement of fleets was also faster than the changes of fleet sizes.The global fish stock and the total number of vessels keep constant at a fast time scale,then a stock-effort dynamical model was established.The dynamical system was reduced by aggregated methods and quantitative methods were used to analyze the existence of positive fixed points,stability and local bifurcation.Finally the global methods were used to analyze the extent of sustainable use of fishery resources.

关 键 词：时间刻度 聚合方法 正平衡点的稳定性 分叉 可行吸引域 

分 类 号：O193[理学—数学] F133.3[理学—基础数学]