本文研究一类以Logistic增长为基础的具有群体防御的水葫芦生态系统.首先得到无脉冲作用的系统定性结论.其次对具有状态反馈控制的脉冲系统,利用微分方程几何理论中后续函数法得到系统的阶一周期解存在的充分条件,证明该周期解是轨道渐近稳定的,同时利用数值模拟讨论了系统生态意义.
This paper discusses certain eco-system of water hyacinth with collectively de- fense based on Logistic growth. First, we gain a qualitative conclusion of systems without im- pulsive function. Further, for systems with state-feedback controls impulse,by using succes- sor function of differential equation geometry theory, the sufficient conditions for the exist- ence and orbitally asymptotic stability of an order one periodic solution are obtained. Finally, applying numerical analog,we discuss the ecological significance of the system.