带交叉扩散项的B-D捕食-食饵模型的全局分歧 |
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引用本文: | 王晓丽,容跃堂,董苗娜,何堤. 带交叉扩散项的B-D捕食-食饵模型的全局分歧[J]. 纺织高校基础科学学报, 2016, 0(3): 319-326. DOI: 10.13338/j.issn.1006-8341.2016.03.008 |
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作者姓名: | 王晓丽 容跃堂 董苗娜 何堤 |
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作者单位: | 西安工程大学 理学院,陕西 西安,710048 |
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基金项目: | 陕西省自然科学基础研究计划项目(2015JM1034) |
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摘 要: | 研究一类带有交叉扩散项的B-D捕食-食饵模型在齐次Dirichlet边界条件下正解的存在性.利用极大值原理得到正解的先验估计;通过分析相关特征值问题,得到两条无界的中性曲线;并借助Crandall-Rabinowitz分歧理论,得出局部分歧正解的存在性,从而将局部分歧延拓为全局分歧.
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关 键 词: | 交叉扩散 捕食-食饵模型 先验估计 全局分歧 |
The global bifurcation for a prey-predator model with cross-diffusion and B-D functional response |
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Abstract: | This paper concerns the existence of positive solutions for a predator-prey model with cross-diffusion and B-D functional response under homogeneous Dirichlet boundary conditions. By the maximum principle,a priori estimate of positive solutions are obtained.By considering the related eigenvalue problems,two unbounded neutral curves are given.Then by Crandall-Rabinowitz bifurcation theory,the existence of positive solutions to a local bifurcation is proved.Finally,the local bifurcation is developed to the global one. |
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Keywords: | cross-diffusion predator-prey model a priori estimate global bifurcation |
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