产生有毒物质的浮游植物—浮游动物离散动力学模型分析  

Discrete Dynamical Analysis for a Toxin Producing Phytoplankton-Zooplankton Model

作　　者：顾恩国[1] 张梅娜[1] 陈博[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）》2013年第2期117-122,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)

摘　　要：从浮游植物与浮游动物的连续动力学模型出发,建立了一个浮游生物的离散动力系统,然后研究了正不动点的存在性、局部稳定性以及关于环境对有毒浮游植物的最大承载能力的局部分叉,并且运用中心流行定理分析了在flip分叉值处不动点的局部稳定性,最后用数值模拟方法验证了不动点的局部分叉,描述了捕捞力度对浮游生物资源的可持续利用的影响.In this paper, a plankton discrete dynamical model is established in light of considering a phytoplanktou and zooplankton continuous model. The existence and local stability of the positive equilibrium, and the local bifurcation about the environmental carrying capacity of toxin producing phytoplankton population are discussed. The center-manifold theorem is used to analyze the local stability of the f/xed point at flip bifurcation value. Finally,the numerical simulation is used to verify the local bifurcations of fixed points, and analyze the influence of harvesting effort on the sustainable utilization of the plankton resources.

关 键 词：正不动点 稳定性 倍周期分叉 Neimark分叉 

分 类 号：O221[理学—运筹学与控制论]