多个体博弈多代共存的公共渔业资源模型及分析  

Analysis of Multi-Agent Game for Multi-Generational Coexistence Fishery Resources Model

作　　者：顾恩国[1] 张兴起[1] 

机构地区：[1]中南民族大学数学与统计学学院,武汉430074

出　　处：《中南民族大学学报（自然科学版）》2010年第2期100-105,共6页Journal of South-Central University for Nationalities：Natural Science Edition

基　　金：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(YZZ06027)

摘　　要：假设渔业资源生长满足多代共存的Logistic模型,利用多个体博弈达到Nash均衡时的捕捞量得到了总收获函数,建立了多个体博弈公共渔业资源的二维动力学模型,使用非线性动力学分析方法对系统的正不动点的存在性、局部稳定性进行了分析,并用数值模拟研究了不动点的局部分叉.使用映射的奇异集理论给出了可行吸引域的定界方法与全局分叉,再结合数值模拟得到了渔业资源不枯竭的条件.In this paper, the growth of fishery resources is supposed as the multi-generational coexistence Logistic model, multi-agent game which satisfies Nash equilibrium conditions is used to get the total harvest function, and the two-dimensional dynamic model of multi-agent games in common fishery resources is established. The non- linear dynamic methods are used to analyze the existence of positive fixed points, local stability of the model, and numerical simulation is used to verify the local bifurcations of fixed points. The singular set theory of mapping is used to get feasible attractive basin boundary and analyze the global bifurcation, and numerical simulation isused to get unexhausted conditions.

关 键 词：渔业资源 多代共存的Logistic模型 NASH均衡 非线性分析 正不动点 局部稳定性 数值模拟 奇异集理论 全局分叉 可持续利用 

分 类 号：O192[理学—数学]