基于Dulac函数的捕食-食饵模型的定性行为

Qualitative Behavior of a Predator-prey Model Based on Dulac Function

为解决传统捕食-食饵模型对定性行为中极限环的不存在性判断时间较长的问题,为此对基于Dulac函数的捕食-食饵模型定性行为进行研究,并对食饵常数投放率进行计算。验证模型定性行为的必然持续性,为平衡位置的计算提供充分必要条件,由Dulac函数判别模型极限环的不存在性,计算出定性行为的平衡点。通过实验论证得出,捕食-食饵模型相比文献[3]模型判断时间缩短0.4min。

In order to solve the problem that the traditional predator-prey model has a long time to determine the non-existence of the limit cycle in qualitative behavior,the qualitative behavior of the predator-prey model based on Dulac function is studied,and the rate of feeding constant is calculated.The necessary continuity of the qualitative behavior of the model is verified,sufficient and necessary conditions are provided for the calculation of the equilibrium position, the absence of the limit cycle of the model is judged by the Dulac function,and the equilibrium point of the qualitative behavior is calculated. Through experimental demonstration,it is concluded that the predator-prey model shortens the judgment time by 0.4 min compared to the model in[3].