Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 1192-1203.

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Complex Dynamics and Stochastic Sensitivity Analysis of a Predator-Prey Model with Crowley-Martin Type Functional Response

Tengfei Wang(),Tao Feng(),Xinzhu Meng*()   

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Shandong Qingdao 266590
  • Received:2019-10-29 Online:2021-08-26 Published:2021-08-09
  • Contact: Xinzhu Meng;;
  • Supported by:
    the NSF of Shandong Province(ZR2019MA003);the Research Fund for the Taishan Scholar Project of Shandong Province


Predator-prey interactions serve a pivotal role in protecting species diversity. In this study, the parameter $λ$ is presented to show the stochastic dynamics of a predator-prey model. The results show that the predator population tends to become extinct if $λ$ < 0. Furthermore, the solution of the prey population converges weakly to an invariant probability distribution. If $λ$>0, we find that the stochastic system admits a unique ergodic stationary distribution. In addition, stochastic sensitivity analysis is proposed to study the effects of noise on the dynamics of predator-prey populations. Our findings suggest that small-intensity noise can suppress population size enlargement, while large-intensity noise can lead to the extinction of populations.

Key words: Predator-prey interaction, Stochastic model, Stochastic sensitivity analysis, Ergodic property, Stationary distribution

CLC Number: 

  • O175