Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (3): 674-688.

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Dynamics of a Stochastic Predator-Prey Model with Pulse Input in a Polluted Environment

Yingjie Fu,Guijie Lan,Shuwen Zhang,Chunjin Wei*()   

  1. School of Sciences, Jimei University, Fujian Xiamen 361021
  • Received:2018-03-13 Online:2019-06-26 Published:2019-06-27
  • Contact: Chunjin Wei
  • Supported by:
    the Fujian Provincial Natural Science Foundation(2016J01667);the Fujian Provincial Natural Science Foundation(2016J05012);the Fujian Provincial Natural Science Foundation(2018J01418)


In this paper, we show a stochastic predator-prey model with pulse input in a polluted environment, the existence and uniqueness of the positive global solution and the boundedness of expectation of the system are all proved, the sufficient conditions for the existence and boundedness of periodical solution are obtained, and it is globally attractive with probability 1, and the threshold of population extinction and persistence in the mean are obtained too. Finally, some numerical simulations are carried out to illustrate the main results.

Key words: Predator-prey system, Pulse toxicant, Random disturbance, Mean boundedness, Globally attractivity

CLC Number: 

  • O175.13