具有修正因子的两种群微分模型的定性分析

A qualitative analysis of two species differential model with modifying factor

目的主要对第一类功能反应函数φ(x)={αx,0<x<x0 αx 0,x>x0增加修正因子b1/(1+βy)后得到的两种群微分模型,对系统进行完整的定性分析。方法运用常微分方程定性理论进行研究。结果得到系统平衡点的性态及极限环不存在条件、极限环存在条件及其惟一性条件,增加修正因子使模型更加准确的描述此类生态系统,最后给出了数值模拟仿真进一步验证定理的准确性。结论完善了此模型的研究。

Aim To introduce a class of differential model which is founded by the first founctional response function φ（x）={αx,0〈x〈x0 αx0,x〉x0 under the modifying factor b1/（1＋βy）.Methods By using the qualitative theory of ordinary differential equations.Results The quality of the equilibrium is discussed,the existence and the uniqueness of the limit cycle in this system are proved.The model is more accurate than model without modifying factor.Computer simulations are carried to confirm the main theorems.Conclusion So the model is developed.