具有恐惧效应、时滞和扩散的随机捕食-食饵模型的动力学分析  

Dynamics Analysis of a Stochastic Predator-Prey Model with Fear Effects,Time Delays and Diffusion

作　　者：刘萍[1] 蒙诚霖 LIU Ping;MENG Chen-lin(School of Mathematics and Statistics,Yunnan University,Kunming 650500,China)

机构地区：[1]云南大学数学与统计学院,云南昆明650500

出　　处：《数学的实践与认识》2023年第4期287-296,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11961078)。

摘　　要：研究了一类具有恐惧效应、时滞及空间扩散的随机捕食-食饵系统.首先,证明系统在任意正初值下有唯一存在的全局正解;其次,通过构造适当的Lyapunov函数,结合伊藤公式和切比雪夫不等式,证明系统的解是随机最终有界的;最后,利用随机微分方程比较定理,分别得到了种群灭绝与平均持续生存的充分条件.This paper deal with a stochastic predator-prey systems with fear effects,time delays and spatial diffusion.Firstly,a unique global positive solution for the system with positive initial value is obtained.Secondly,by constructing appropriate Lyapunov function,combined with Ito's formula and Chebyshev's inequality,we obtain that the solution of system is stochastically ultimate boundedness.Finally,by using the comparison theorem of stochastic differential equations,sufficient conditions for the extinction of populations and persistence in the mean of the solution for the system are obtained,respectively.

关 键 词：随机捕食-食饵系统 恐惧效应 扩散 持久性与灭绝性 

分 类 号：O175[理学—数学] Q141[理学—基础数学]