一类具有年龄结构的麦蚜-瓢虫模型的全局分析

Global Qualitative Analysis on a Wheat Aphid-Ladybug Model with Age Structured

研究了一个具有年龄结构的麦蚜-瓢虫模型,其中麦蚜种群被分成两个年龄段,瓢虫种群被分成三个年龄段．应用定性理论可以证明:通过这两个种群的交互作用,可以导致麦蚜种群和瓢虫种群都灭绝或瓢虫种群灭绝,或这两个种群能以正平衡态或振动解的形式共存．通过计算,本文表明这个简单的系统可以产生非常复杂的动力学行为．在这种情形下,要想通过初始值来预测种群的数量是不可能的．应用MATLAB软件,本文展示了这个复杂的动力学行为．

In this paper, we investigate the wheat aphid-ladybug model with age structure, where the wheat aphid species has two life stages and the ladybug species has three life stages. By the qualitative theory theory, we shows that the interactions bctween the two species may lead to that wheat aphid species and ladybug species are all extinct, or the ladybug species is extinct, or wheat aphid species and ladybug species may be coexistence in the form of positive steady state or oscillatory solutions. Via calculating, we point out the simple populations system may producc very complicated dynamics behavior. This paper presents examples to illustrate the above conclusions by using MATLAB software.