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.

scholarly journals Existence, Stationary Distribution, and Extinction of Predator-Prey System of Prey Dispersal with Stochastic Perturbation

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Li Zu ◽  
Daqing Jiang ◽  
Fuquan Jiang
Keyword(s):  
Numerical Simulation ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Ergodic Property ◽  
Unique Positive Solution ◽  
Initial Value ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

We consider a predator-prey model in which the preys disperse amongnpatches (n≥2) with stochastic perturbation. We show that there is a unique positive solution and find out the sufficient conditions for the extinction to the system with any given positive initial value. In addition, we investigate that there exists a stationary distribution for the system and it has ergodic property. Finally, we illustrate the dynamic behavior of the system withn=2via numerical simulation.

scholarly journals Persistence and Nonpersistence of a Food Chain Model with Stochastic Perturbation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Haihong Li ◽  
Fuzhong Cong ◽  
Daqing Jiang ◽  
Hongtu Hua
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Food Chain ◽  
Stochastic Perturbation ◽  
Chain Model ◽  
Unique Positive Solution ◽  
Predator Prey ◽  
Time Average ◽  
Food Chain Model

We analyze a three species predator-prey chain model with stochastic perturbation. First, we show that this system has a unique positive solution and itspth moment is bounded. Then, we deduce conditions that the system is persistent in time average. After that, conditions for the system going to be extinction in probability are established. At last, numerical simulations are carried out to support our results.

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.

Analysis on stochastic predator-prey model with distributed delay

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
C. Gokila ◽  
M. Sambath
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Disease In Prey ◽  
Stochastic Lyapunov Function

Abstract In the present work, we consider a stochastic predator-prey model with disease in prey and distributed delay. Firstly, we establish sufficient conditions for the extinction of the disease and also permanence of healthy prey and predator. Besides, we obtain the condition for the existence of an ergodic stationary distribution through the stochastic Lyapunov function. Finally, we provide some numerical simulations to validate our theoretical findings.

scholarly journals Global Stability of a Stage-Structured Predator-Prey Model with Stochastic Perturbation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Liu Yang ◽  
Shouming Zhong
Keyword(s):  
Stochastic Model ◽  
Positive Solution ◽  
Stochastic Perturbation ◽  
Stage Structure ◽  
Positive Equilibrium ◽  
Deterministic System ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Positive Equilibrium Point

This paper is concerned with a new predator-prey model with stage structure on prey, in which the immature prey and the mature prey are preyed on by predator. We think that the model is more realistic and interesting than the one in which only the immature prey or the mature prey is consumed by predator. Our work shows that the stochastic model and its corresponding deterministic system have a unique global positive solution and the positive solution is global asymptotic stability for each model. If the positive equilibrium point of the deterministic system is globally stable, then the stochastic model will preserve the nice property provided that the noise is sufficiently small. Results are analyzed with the help of graphical illustrations.

scholarly journals Hopf bifurcation in a diffusive predator–prey model with Smith growth rate and herd behavior

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Heping Jiang ◽  
Huiping Fang ◽  
Yongfeng Wu
Keyword(s):  
Hopf Bifurcation ◽  
Neumann Boundary ◽  
Herd Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Prey System ◽  
Prey Model ◽  
Homogeneous Neumann Boundary Condition ◽  
The Stability

Abstract This paper mainly aims to consider the dynamical behaviors of a diffusive delayed predator–prey system with Smith growth and herd behavior subject to the homogeneous Neumann boundary condition. For the analysis of the predator–prey model, we have studied the existence of Hopf bifurcation by analyzing the distribution of the roots of associated characteristic equation. Then we have proved the stability of the periodic solution by calculating the normal form on the center of manifold which is associated to the Hopf bifurcation points. Some numerical simulations are also carried out in order to validate our analysis findings. The implications of our analytical and numerical findings are discussed critically.

scholarly journals Permanence and global stability of positive solutions of a nonautonomous discrete ratio-dependent predator-prey model

2005 ◽  
Vol 2005 (2) ◽  
pp. 135-144 ◽  
Author(s):  
Hai-Feng Huo ◽  
Wan-Tong Li
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Positive Solution ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

We first give sufficient conditions for the permanence of nonautonomous discrete ratio-dependent predator-prey model. By linearization of the model at positive solutions and construction of Lyapunov function, we also obtain some conditions which ensure that a positive solution of the model is stable and attracts all positive solutions.

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