具有干扰的捕食与被捕食模型的定性分析

The qualitative analysis of interference with the predatcr-prey model

目的研究具有干扰的捕食与被捕食模型的全局稳定性及极限环的存在惟一性。方法利用特征值定理,构造Lyapunov函数与张芷芬惟一性定理。结果得到模型正平衡态的局部渐近稳定性及极限环的存在惟一性的充分条件。结论解决了陈兰孙对模型提出的极限环存在及惟一性的猜想。

Aim To study interference with the Predator-prey of model of global stability and the presence of limit cycles. Methods Applying the eigenvalue theory, constructing Liapunov function and the uniqueness theorem of Zhifen. Results The sufficient conditions of the local asympototic stability of equilibrium model, global stability and the uniqueness of the limit cycles are derived. Conclusion Solving the conjecture about the presence of limit cycles by Lansun Chen.