具有植化相克效应的浮游植物微分代数模型分岔  

The Dynamics in a Harvested Differential-algebraic Allelopathic Phytoplankton Model

作　　者：周波[1] 冯毅夫[1,2] 刘超[1,2] 

机构地区：[1]吉林师范大学生命科学学院,吉林四平136000 [2]东北大学系统科学研究所,辽宁沈阳110004

出　　处：《生物数学学报》2009年第3期496-500,共5页Journal of Biomathematics

摘　　要：应用微分代数系统理论与分岔理论,本文研究了具有植化相克效应与捕捞作用的浮游植物的微分代数模型的动态行为以及相关的生态控制问题。研究表明该类生态系统的失稳与微分代数模型在正平衡点处的动态行为有关,同时对该生态系统进行的捕捞行为也会对系统的稳定性产生影响。为了保证该类生态系统稳定,本文设计了一类状态反馈控制器,最后用数值例子说明了得到定理的有效性。A harvested allelopathic two-species phytoplankton ecosystem is investigated by a differential-algebraic model. By using the differential-algebraic system theory and bifurcation theory, local stability of the proposed model around the interior equilibrium is investigated. Furthermore, the instability mechanism of the proposed model due to variation of economic interest of harvesting is studied. With the purpose of stabilizing the proposed model around the interior equilibrium and maintaining the economic interest of harvesting at an ideal level, astate feedback controller is designed. Finally, numerical simulations are carried out to illustrate the effectiveness of the designed controller.

关 键 词：微分代数模型 奇异诱导分岔 捕捞行为 经济利益 

分 类 号：O23[理学—运筹学与控制论]