| 摘要: |
| 在Logistic模型的基础上增加天敌的胁迫项，构造了天敌胁迫下食饵种群的动态模型。在食饵种群的增长量和天敌的捕食量达到动态平衡的情况下，推导出食饵种群动态的尖角突变模型。运用突变分析的方法，解释了食饵种群在天敌胁迫下也有可能爆发的生态现象。尖角突变模型中的复合控制变量无需坐标转化即可判断系统所处的状态。从理论上解决了以往研究复合控制变量时参数转化的问题。参数简化后可得到折叠突变模型。 |
| 关键词: 突变理论 尖角突变模型 种群动态 折叠突变模型 |
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| 基金项目:国家自然科学基金资助项目(39970112；30470268)；陕西省重点资助项目(2001SM01) |
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| Catastrophe Analysis of A Predator Model with Prey |
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| Abstract: |
| Prey population growth can be modeled with the Logistic function.When one prey item is added,we get a prey population growth model with predators intimidate.Under the condition of the growth rate of prey equal to the prey rate,cusp catastrophe model is deduced.Catastrophe analysis method is used to interpret ecological catastrophe phenomena and judge the state of prey population by control variable without changing,thus the fold catastrophe model with predigest parameter is obtained. |
| Key words: catastrophe theory cusp catastrophe model population dynamic fold catastrophe model |
