Stability of a three-species stochastic delay predator–prey system with Lévy noise

2018 ◽  
Vol 502 ◽  
pp. 492-505 ◽  
Author(s):  
Jian Wu
Keyword(s):  
Lévy Noise ◽  
Stochastic Delay ◽  
Predator Prey ◽  
Prey System ◽  
Levy Noise

Two impulsive stochastic delay single-species models incorporating Lévy noise

2018 ◽  
Vol 58 (1-2) ◽  
pp. 721-753 ◽  
Author(s):  
Huibin Lv ◽  
Zhijun Liu ◽  
Zuxiong Li ◽  
Lianwen Wang ◽  
Dashun Xu
Keyword(s):  
Single Species ◽  
Lévy Noise ◽  
Stochastic Delay ◽  
Levy Noise

Analysis of a stochastic predator–prey model with prey subject to disease and Lévy noise

2019 ◽  
Vol 19 (05) ◽  
pp. 1950038
Author(s):  
Meihong Qiao ◽  
Shenglan Yuan
Keyword(s):  
Positive Solution ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Lévy Noise ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Stochastic Boundedness ◽  
Prey Model ◽  
Global Positive Solution ◽  
Levy Noise

We consider a non-autonomous predator–prey model, with prey subject to the disease and Lévy noise. We show the existence of global positive solution and stochastic boundedness. Then, we examine the asymptotic properties of the solution. Finally, we offer sufficient conditions for persistence and extinction.

scholarly journals Analysis of Stochastic Delay Predator-Prey System with Impulsive Toxicant Input in Polluted Environments

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Meng Liu
Keyword(s):  
Polluted Environment ◽  
Stochastic Delay ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Time Average

A stochastic delay predator-prey model in a polluted environment with impulsive toxicant input is proposed and studied. The thresholds between stability in time average and extinction of each population are obtained. Some recent results are extended and improved greatly. Several simulation figures are introduced to support the conclusions.

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