JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (10): 54-66.doi: 10.6040/j.issn.1671-9352.0.2022.635

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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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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

CLC Number: 

  • O175

Table 1

Biological meaning of each parameter"

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

Table 2

Parameter values of Model (2)"

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

Fig.1

Time series plots of Model (2) with σ1=1.9, σ2=1.2"

Fig.2

Persistence of Model (2) with σ1=0.1, σ2=0.1"

Fig.3

Probability density functions of x(t) and y(t) of Model (2)"

Fig.4

Time series plots of Model (2) with f=0, 0.2, 0.8"

Fig.5

Time series plots of Model (2) with f=0.8, σ1=0.8, σ2=0.8"

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