具有Monod-Haldane功能反应的一类食物链模型的动力学行为  

On the Dynamics of a Food Chain with Monod-Haldane Functional Response

作　　者：王育全[1] 刘来福[2] 

机构地区：[1]南京财经大学应用数学系,南京210003 [2]北京师范大学数学系,北京100875

出　　处：《数学物理学报（A辑）》2007年第1期79-89,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(10371037)资助

摘　　要：该文研究了一个由食饵种群、捕食者种群和杂食者种群所构成的食物链系统,其捕食功能反应为Monod-Haldane功能反应．应用定性分析和Hopf分支理论,得到了该系统边界平衡点的全局稳定性和周期解存在性的判别准则．为了概括和归类这个系统的全局动力学行为,该文得到了具有不同动力学行为的参数区域．应用MATLAB软件,该文提供了一个例子来展示这些结论,并且表明:这个系统能够产生非常复杂的动力学行为．A dynamics model of food chain for three species including prey, predator and toppredator is studied. The Monod-Haldance functional response is used in the food chain system. By applying qualitative analysis and Hopf bifurcation theory, criteria are derived for global stability of the boundary equilibria, existence of periodic orbits and persistence of the system. To summarize and classify the global dynamics of the system, the parameters regions with different dynamics behavior are derived. According to the regions, the authors show that the system can lead to a very complicated dynamics behavior and present an example to illustrate the conclusions by using MATLAB software.

关 键 词：食物链模型 全局稳定 周期解 HOPF分支 

分 类 号：O175.12[理学—数学]