带交叉扩散项的捕食模型正稳态解的存在性分析

Existence of Positive Steady-state Solution for a Prey-Predator Model with Cross-Diffusion

讨论了一类具有交叉扩散项的Holling-Tanner捕食-食饵生态模型的正稳态解的存在性。利用最大值原理给出了此模型正解的先验估计,进一步利用特征值和单特征值的局部分歧理论,以物种v的增长率b作为分歧参数,证明了系统在半平凡解附近出现分歧。

The existence of positive steady-state solution for a prey-predator model with cross-diffusion was dis- cussed in this paper. The prior estimate to the positive solutions of the model was given by means of maximum principle. Furthermore, treating the increase rate b as the bifurcation parameter, the bifurcation from the semi- trivial solutions was obtained according to the local bifurcation theory with eigenvalues.