生物学中一类带有扩散项模型的全局分歧研究

Global Bifurcation of a Model with Diffusion Terms in Biology

研究了一类带扩散项的pioneer-climax模型在Neumann边界条件下的共存态问题。首先,给出了平衡态方程解的先验估计。其次,利用分歧理论和度理论,结合极值原理,以d为分歧参数,得到系统非常数正解的存在性,同时得出局部分歧可延拓为全局分歧。再次,详细地描述了非常数正解的全局分歧结构。最后,讨论了连通分支Γ伸向无穷。

The coexistence of a diffusive pioneer-climax species model is investigated under the Neumann boundary condition.First,the priori estimates of steady-state solutions are given.Then,based on treating d as bifurcation parameter,the existence of positive steady-state solution is derived mainly by using of the global bifurcation theory,the degree theory and the maximum principle.Also the local bifurcation can be extended to global bifurcation.Moreover,a detailed description for the global bifurcation of the set of the non-constant positive solution is given.Finally,the continuum Γj joins up with infinity is discussed.