基于捕鱼期与休渔期交替变换及两类功能反应的捕食-食饵模型的动力学行为研究  

The Study of the Dynamic Behaviors of a Predator-Prey Model Based on Alternation of Fishing Season and Fishing Ban Season,and Two Kinds of Functional Responses

作　　者：王晓雯 张龙[1] 杭磊 WANG Xiao-wen;ZHANG Long;HANG Lei(College of Mathematics and System Science,Xinjiang University,Urumqi 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《数学的实践与认识》2023年第11期120-128,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11861065,11361059,11771373,11702237);新疆维吾尔自治区重点实验室项目(2016D03022);新疆大学博士科研启动资金(BS160204);新疆大学博士创新项目(XJUBSCX-2017005);自治区普通高等学校科研计划项目(XJEDU2017T001)。

摘　　要：本文研究了一类捕鱼期、休渔期交替变换,带有HollingⅡ型功能反应与Beddington-DeAngelis型功能反应的两种群的捕食食饵模型.主要研究系统有界性、持久性、灭绝性等动力学行为,通过构造合适的Lyapunov函数来研究平衡点的全局渐近稳定性,并建立了相应的判定准则,最后通过数值模拟验证了理论结果的有效性.This paper mainly studied the fishing season,fishing ban season alternating with Holling Ⅱ functional response and Beddington-Deangelis functional response of two species predator-prey model with harvesting.We mainly study the dynamic behaviors such as boundedness,persistence,and extinction of the system.By constructing appropriate Lyapunov function,we study the global asymptotic stability of the equilibrium,and establish corresponding criteria.Finally,the theoretical results are illustrated by numerical simulation.

关 键 词：有界性 持久性 灭绝性 全局渐近稳定性 

分 类 号：O175[理学—数学] S931.1[理学—基础数学]