Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 71, pp. 1-17

Title: Asymptotic behavior of stochastic three-species predator-prey systems
       with white and Levy noise 
       
Authors: Yihan Zhao   (Chongqing Normal Univ., Chongqing, China)
         Yuanpei Xia  (Chongqing Normal Univ., Chongqing, China)
         Zhichun Yang (Chongqing Normal Univ., Chongqing, China)

Abstract:
 In this article, we propose a three-species prey-predator system with Holling II
 functional response and stochastic perturbations involving white noise and
 Levy noise. Firstly, we study the existence and uniqueness of a global positive
 solution  and stochastic ultimate boundedness. Then, we obtain sufficient conditions
 for stability, extinction, strongly persistence in the mean and stochastic permanence
 in the sense of probability for the stochastic system.
 The results show that both white noise and Levy noise may change the asymptotic
 properties of the population system. Finally, some examples that chaotic dynamics
 can be influenced by stochastic noises.
 
Submitted February  6, 2020. Published July 06, 2020.
Math Subject Classifications: 34D20, 92D25, 60H10.
Key Words: Predator-prey system; Levy noise; white noise; extinction;
           stochastic permanence.