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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (10): 54-66.doi: 10.6040/j.issn.1671-9352.0.2022.635

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具有恐惧效应和Crowley-Martin功能反应的随机捕食模型的动力学

张钰珂(),孟新柱*()   

  1. 山东科技大学数学与系统科学学院, 山东 青岛 266590
  • 收稿日期:2022-11-27 出版日期:2023-10-20 发布日期:2023-10-17
  • 通讯作者: 孟新柱 E-mail:zhangyukekkk@163.com;mxz721106@sdust.edu.cn
  • 作者简介:张钰珂(1998—)，女，硕士研究生，研究方向为种群动力学. E-mail: zhangyukekkk@163.com
  • 基金资助:
    国家自然科学基金资助项目(12271308);山东省自然科学基金资助项目(ZR2019MA003);山东省泰山学者计划资助项目

Dynamics of a stochastic predation model with fear effect and Crowley-Martin functional response

Yuke ZHANG(),Xinzhu MENG*()   

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China
  • Received:2022-11-27 Online:2023-10-20 Published:2023-10-17
  • Contact: Xinzhu MENG E-mail:zhangyukekkk@163.com;mxz721106@sdust.edu.cn

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摘要：

研究具有恐惧效应和Crowley-Martin功能反应的随机捕食者-食饵模型。证明随机模型的全局正解的存在唯一性和解的有界性, 利用随机定性分析的方法研究种群平均持久和灭绝的充分条件。通过巧妙地构建合适的李雅普诺夫函数, 分类研究系统的遍历平稳分布的存在唯一性。最后, 数值模拟验证恐惧效应和白噪声对种群动力学理论结果的影响。

关键词: Crowley-Martin功能反应, 全局正解, 随机定性分析, 遍历平稳分布

Abstract:

A stochastic predator-prey model with fear effect and Crowley-Martin functional response is studied. We first give the existence and uniqueness of global positive solutions and the boundedness of solutions on the stochastic model. We explore sufficient conditions for the persistence in mean and the extinction of the populations by using stochastic qualitative analysis theory. The existence of unique ergodic stationary distribution is proved by establishing suitable Lyapunov functions. Finally, numerical simulations are conducted to reveal the effects of fear and white noise on the theoretical results of population dynamics.

Key words: Crowley-Martin functional response, global positive solution, stochastic qualitative analysis, ergodic stationary distribution

中图分类号: 

  • O175

表1

各参数的生物学意义"

参数 含义
r 内禀增长率
f 由捕食者引起的恐惧程度
δ 食饵的密度制约系数
β 捕食率
q 能量转换率
d 捕食者的死亡率
h 捕食者的密度制约系数

表2

模型(2) 的参数取值"

参数 r f β δ q d h a b
取值 1.5 0.2 0.5 0.01 0.9 0.042 0.2 2 2

图1

σ1=1.9, σ2=1.2时, 模型(2)的时间序列图"

图2

σ1=0.1, σ2=0.1时模型(2)的持久性"

图3

模型(2)中x(t)和y(t)的概率密度函数图"

图4

f为0、0.2、0.8时模型(2)的时间序列图"

图5

f=0.8, σ1=0.8, σ2=0.8时, 模型(2)的时间序列图"

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