Global Qualitative Analysis of a New Monod Type Chemostat Model With Delayed Growth Response and Pulsed Input in a Polluted Environment
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摘要: 考虑了一类新的污染环境下具有时滞增长反应及脉冲输入的Monod恒化器模型.运用离散动力系统的频闪映射,获得了一个‘微生物灭绝’周期解,进一步获得了该周期解全局吸引的充分条件.运用脉冲时滞泛函微分方程新的计算技巧,证明了系统在适当的条件下是持久的,结论还表明该时滞是“有害”时滞.Abstract: A new Monod type chemostat model is considered with time delay and pulsedinput concentration of the nutrient in a polluted environment. Using the discrete dynamical system deter mined by the stroboscopic map, a-microorg anismex tinction. periodic solution is obtained. Further more, the sufficient conditions for the global attractivity of the micro organism-extinction periodic solution are established. Using new computational techniques for impulsive and delayed differential equation, it is proved that the system is permanent under appropriate conditions. The results show that time delay is "profitless".
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Key words:
- permanence /
- impulsive input /
- chemostat model /
- time delay for growth response /
- extinction
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