Periodic Solution and Stationary Distribution of Stochastic Predator–Prey Models with Higher-Order Perturbation

2017 ◽  
Vol 28 (2) ◽  
pp. 423-442 ◽  
Author(s):  
Qun Liu ◽  
Daqing Jiang
Keyword(s):  
Periodic Solution ◽  
Stationary Distribution ◽  
Higher Order ◽  
Order Perturbation ◽  
Predator Prey ◽  
Predator Prey Models

scholarly journals Periodic solution and stationary distribution for stochastic predator-prey model with modified Leslie-Gower and Holling type II schemes

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1383-1402
Author(s):  
Qixing Han ◽  
Liang Chen ◽  
Daqing Jiang
Keyword(s):  
Periodic Solution ◽  
Computer Simulations ◽  
Stationary Distribution ◽  
Autonomous System ◽  
Sufficient Conditions ◽  
Type Ii ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Autonomous Case

In this paper, a stochastic predator-prey system with modified Leslie-Gower and Holling type II schemes is studied. For the autonomous case, we prove that the system has a stationary distribution under some parametric restrictions. We also obtain conditions for the non-persistence of the system, and the results are illustrated by computer simulations. For the non-autonomous system with continuous periodic coefficients, sufficient conditions which guarantee the existence of periodic solution of the system are established.

The global dynamics of stochastic Holling type II predator-prey models with non constant mortality rate

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5811-5825
Author(s):  
Xinhong Zhang
Keyword(s):  
Mortality Rate ◽  
Stochastic Model ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Global Dynamics ◽  
Type Ii ◽  
Predator Prey ◽  
Persistence In The Mean ◽  
The Mean ◽  
Predator Prey Models

In this paper we study the global dynamics of stochastic predator-prey models with non constant mortality rate and Holling type II response. Concretely, we establish sufficient conditions for the extinction and persistence in the mean of autonomous stochastic model and obtain a critical value between them. Then by constructing appropriate Lyapunov functions, we prove that there is a nontrivial positive periodic solution to the non-autonomous stochastic model. Finally, numerical examples are introduced to illustrate the results developed.

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