scholarly journals The Asymptotic Behavior of a Stochastic Predator-Prey System with Holling II Functional Response

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Zhenwen Liu ◽  
Ningzhong Shi ◽  
Daqing Jiang ◽  
Chunyan Ji
Keyword(s):  
Population Dynamics ◽  
Asymptotic Behavior ◽  
Positive Solution ◽  
Functional Response ◽  
Dynamics Model ◽  
Unique Positive Solution ◽  
Predator Prey ◽  
Prey System ◽  
Population Dynamics Model ◽  
Holling Ii Functional Response

We discuss a stochastic predator-prey system with Holling II functional response. First, we show that this system has a unique positive solution as this is essential in any population dynamics model. Then, we deduce the conditions that there is a stationary distribution of the system, which implies that the system is permanent. At last, we give the conditions for the system that is going to be extinct.

scholarly journals Dynamics of a Stochastic Cooperative Predator-Prey System with Beddington-DeAngelis Functional Response

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Dongwei Huang ◽  
Yu Li ◽  
Yongfeng Guo
Keyword(s):  
Asymptotic Stability ◽  
Positive Solution ◽  
Functional Response ◽  
Dynamic Properties ◽  
Deterministic System ◽  
Unique Positive Solution ◽  
Initial Value ◽  
Predator Prey ◽  
Prey System ◽  
Stochastically Bounded

Stochastic cooperative predator-prey system with Beddington-DeAngelis functional response is studied. It presents an investigation of dynamic properties of the system. Our results show that there exists a unique positive solution to the system for any positive initial value, and the positive solution is stochastically bounded. Moreover, under some conditions, we analyze global asymptotic stability of the positive solutions. With small environmental noises, the stochastic system is getting more similar to the corresponding deterministic system. Neither of the species in the system will die out. Finally, simulations are carried out to conform to our result.

scholarly journals Permanence of Periodic Predator-Prey System with Functional Responses and Stage Structure for Prey

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Can-Yun Huang ◽  
Min Zhao ◽  
Hai-Feng Huo
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Ii Functional Response

A stage-structured three-species predator-prey model with Beddington-DeAngelis and Holling II functional response is introduced. Based on the comparison theorem, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. An example is also presented to illustrate our main results.

scholarly journals The Stability of Solutions for a Fractional Predator-Prey System

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yingjia Guo
Keyword(s):  
Lyapunov Stability ◽  
Lyapunov Stability Theory ◽  
Positive Equilibrium ◽  
Stability Of Solutions ◽  
Unique Positive Solution ◽  
Predator Prey ◽  
Prey System ◽  
Fractional System ◽  
The Stability ◽  
Holling Ii Functional Response

We study a class of fractional predator-prey systems with Holling II functional response. A unique positive solution of this system is obtained. In order to prove the asymptotical stability of positive equilibrium for this system, we study the Lyapunov stability theory of a fractional system.

scholarly journals Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Haihong Li ◽  
Daqing Jiang ◽  
Fuzhong Cong ◽  
Haixia Li
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Stationary Distribution ◽  
Stochastic Perturbation ◽  
Unique Positive Solution ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Time Average

We analyze a predator prey model with stochastic perturbation. First, we show that this system has a unique positive solution. Then, we deduce conditions that the system is persistent in time average. Furthermore, we show the conditions that there is a stationary distribution of the system which implies that the system is permanent. After that, conditions for the system going extinct in probability are established. At last, numerical simulations are carried out to support our results.

Randomized 2-Species Predator-Prey System with Functional Response

2014 ◽  
Vol 1033-1034 ◽  
pp. 1373-1376
Author(s):  
Yan Qiu Li ◽  
Hai Long Gao
Keyword(s):  
Differential Equation ◽  
Lyapunov Function ◽  
Stochastic Differential Equation ◽  
Positive Solution ◽  
Functional Response ◽  
Finite Time ◽  
Simple Assumption ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

This paper discusses a randomized Predator-Prey model with Functional Response. Using results from lyapunov function, we show that the positive solution of the associated stochastic differential equation does not explode to infinity in a finite time under simple assumption .It is shown to improve existing results.

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