生物学中一类带有扩散项模型的全局分歧研究

摘要

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Γj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.