具有常数投放的Beddington-DeAngelis型捕食模型的定性分析  

Qualitative Analysis of a Predator-prey Model with Beddington-DeAngelis Functional Response and Constant Inputs

作　　者：夏娟 冯光庭 张兴安[1] 梁桂珍 XIA Juan;FENG Guang-ting;ZHANG Xing-an;LIANG Gui-zhen(School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;School of Mathematics and Statistics, Hubei University of Education, Wuhan 430205, China;School of Mathematics and Information Science, Xinxiang 453003, China)

机构地区：[1]华中师范大学数学与统计学学院,湖北武汉430079 [2]湖北第二师范学院数学与经济学院,湖北武汉430205 [3]新乡学院数学与信息科学学院,河南新乡453003

出　　处：《数学的实践与认识》2018年第7期279-285,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11371161);湖北省自然科学基金(2013CFB013)

摘　　要：利用常微分方程定性和稳定性理论对具有Beddington-DeAngelis型功能反应函数的、食饵种群具有常数投放的捕食一被捕食模型进行了研究，得到解全局稳定和极限环存在的条件，剖析了相应的生态意义，并对特定系数下的系统进行了模拟．ordinary differential equations DeAngelis type functional response, whose to study predator - prey model with Beddingtonprey population has a constant stocking rate, thus we can obtain the existing conditions of global stability of equilibrium point and limit cycle, which is of great significance for rational use and protection of natural resources, and to promote the sustainable development of ecological system. We further analyze the ecological significance of the corresponding system and use Mathematical to simulate the model, when coefficient is given.

关 键 词：Beddington-DeAngelis型功能反应函数 常数投放 全局稳定 极限环 

分 类 号：O175[理学—数学]