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比率依赖型捕食扩散模型的一个注记

ISSN号：1003-7985
期刊名称：《东南大学学报：英文版》
时间：0
分类：O175.26[理学—数学;理学—基础数学]
作者机构：[1]东南大学数学系,南京210096, [2]盐城师范学院数学系,盐城224002
相关基金：The National Natural Science Foundation of China （No. 10471022）, the Natural Science Foundation of Higher Education Institutions of Jiangsu Province （ No. 05KJB110144）. Acknowledgement The authors are greatly grateful to their supervisor Professor Wang Mingxin for his helpful suggestions on this paper.

关键词：比率依赖型捕食模型, 全局渐近稳定, 比较原理, 迭代, ratio-dependent predator-prey model, global stability, comparison principle, iteration

中文摘要：

讨论了在齐次Neumann边界条件下具有比率依赖型捕食反应扩散模型．应用比较原理和建立与正解的上下确界相关的迭代格式，得到了一些改进的结果，即惟一的正常数平衡态是全局渐近稳定的.该结果说明了2种群最终在空间上均匀分布．所提出的方法也适用于其他一些模型．应用于讨论一些反应扩散系统非正常数平衡态的不存在性，该方法相当简单但是十分有效．

英文摘要：

Subject to the homogeneous Neumann boundary condition, a ratio-dependent predator-prey reaction diffusion model is discussed. An improved result for the model is derived, that is, the unique positive constant steady state is the global stability. This is done using the comparison principle and establishing iteration schemes involving positive solutions supremum and infimum. The result indicates that the two species will ultimately distribute homogeneously in space. In fact, the comparison argument and iteration technique to be used in this paper can be applied to some other models. This method deals with the not-existence of a non-constant positive steady state for some reaction diffusion systems, which is rather simple but sufficiently effective.

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