文献类型：期刊文献

中文题名：一类非局部时滞捕食者-食饵扩散模型的空间动力学

英文题名：Spatial dynamics of a non-local and delayed reaction-diffusion predator-prey model

作者：张忠文[1]

第一作者：张忠文

机构：[1]甘肃中医学院理科教学部,兰州730000

第一机构：甘肃中医药大学定西校区

年份：2015

卷号：51

期号：2

起止页码：266

中文期刊名：兰州大学学报（自然科学版）

外文期刊名：Journal of Lanzhou University(Natural Sciences)

收录：CSTPCD;;Scopus;北大核心:【北大核心2014】；CSCD:【CSCD2015_2016】；

基金：国家自然科学基金项目(11271172)

语种：中文

中文关键词：捕食者-食饵模型;非局部时滞;Beverton-Holt函数;波动方法;全局吸引性

外文关键词：predator-prey model; fluctuation method and time-delayed; Beverton-Holt function; fluctuation method; global attractivity

摘要：考虑一类带阶段结构的扩散捕食者食饵模型,其中食饵个体经历两个生命阶段,未成熟和成熟阶段,捕食者生物量的转化有一个延迟,食饵生物量的增长遵循一般化的Beverton-Holt函数.就非局部椭圆特征问题的主特征值,建立一致持久性与全局灭绝性.利用波动方法,给出唯一正常数稳态解的全局吸引性.
A nonlocal and time-delayed reaction-diffusion predator-prey model was studied, where prey individuals undergo two stages, i.e. immature and mature, and the conversion of consumed from prey biomass to predator biomass has a retardation. The growth of the prey population obeys general Beverton-Holt function. By discussing the principal eigenvalue of nonlocal elliptic problems, we showed an explicit expression of the principal eigenvalue, the sufficient conditions for the uniform persistence and global extinction for the model could be established. By the fluctuation method, the global attractivity of the unique positive constant steady state was obtained.