News & Announcements
Links
Asymptotic Behavior of a Stochastic Predator-prey Model with Beddington-DeAngelis Functional Response and L\'{e}vy Jumps
  
View Full Text  View/Add Comment  Download reader
KeyWord:Stochastic predator-prey model; Beddington-DeAngelis functional response; L\'{e}vy jump; Extinction; Persistence
Author NameAffiliation
Yaru Guo School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan, Shanxi 030006, China 
Shulin Sun School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan, Shanxi 030006, China 
Hits: 16
Download times: 13
Abstract:
      A stochastic two-prey-one-predator model with Beddington-DeAngelis functional response and L\'{e}vy jumps is proposed and investigated in this paper. First of all, we prove the existence and uniqueness of the global positive solution, and stochastic ultimate boundedness of the solution. Next, under a simple assumption, by using It\^{o} formula and other important inequalities, some sufficient conditions are established to ensure the extinction and persistence in the mean of the system. The results show that neither strong white noise nor L\'{e}vy noise is conducive to the persistence of the population. Finally, the theoretical results are verified by numerical simulations.