具有恐惧效应和Holling Ⅲ功能性反应的随机捕食-食饵系统  

Stochastic Predator-Prey System with Fear Effect and Holling-Type III Functional Response

作　　者：汪秋分 张树文 Wang Qiufen;Zhang Shuwen(School of data science and computer science,Xiamen Institute of Technology,Fujian Xiamen 361021;School of Science,Jimei University,Fujian Xiamen 361021)

机构地区：[1]厦门工学院数据科学与计算机学院,福建厦门361021 [2]集美大学理学院,福建厦门361021

出　　处：《数学物理学报（A辑）》2024年第5期1380-1391,共12页Acta Mathematica Scientia

基　　金：厦门工学院基于大数据的模糊系统理论及其应用科研创新团队(KYTD202005);厦门工学院校级课程建设项目“数学建模”(AL2019002)。

摘　　要：该文研究了一类具有恐惧效应和Holling Ⅲ功能反应的随机捕食-食饵系统.首先,证明了在任意给定正初始值下,系统全局正解的存在唯一性与均值有界性及随机最终有界性;其次,研究了食饵种群和捕食者种群灭绝和平均持续生存的充分条件,并构造Lyapunov函数证明了系统存在平稳分布及遍历性;最后,通过数值模拟验证了文章的结果.A stochastic predator-prey system with fear effect and Holling-type III functional response is studied.Firstly,the existence and uniqueness of global positive solutions,mean boundedness and stochastic ultimate boundedness of the system for any given positive initial value are proved.Secondly,the sufficient conditions for extinction and persistence in mean of the prey and predator populations are obtained,and Lyapunov function is constructed to prove the existence of stationary distribution and ergodicity.Finally,the results are verifed by numerical simulations.

关 键 词：恐惧效应 捕食-食饵系统 HollingⅢ功能反应 灭绝性与持久性 平稳分布 

分 类 号：O211.63[理学—概率论与数理统计]