一类捕食-食饵模型平衡解的分歧性研究

文章研究了一类捕食者能产生休眠卵的捕食-食饵模型在第二边界条件下的平衡态问题.首先,给出了其正解的先验估计和平衡解 的稳定性结论,并利用能量方法得到其非常数正解的不存在性；其次,在一维情况下,证明了以 为分歧参数的条件下,系统在正常数平衡解 附近出现分歧现象.

Research on the bifurcation of the steady-state solutions for a predator-prey model

The steady-state system of a predator-prey model which the predator can produce resting eggs are investigated under the second boundary conditions.First,a priori estimates for positive solutions and the steady-state solutions(u*,v*)’s stability are established,the non-existence of non-constant positive steady states is given by using the energy method.Second,in one dimensional case,the bifurcation from the steady-state solutions(u*,v*) are obtained by treating a as a bifurcation parameter.