scholarly journals Stationary distribution and pathwise estimation of n-species mutualism system with stochastic perturbation

2016 ◽  
Vol 09 (04) ◽  
pp. 1936-1943 ◽  
Author(s):  
Weiwei Fang ◽  
Qixing Han ◽  
Xiangdan Wen ◽  
Qiuyue Li
Keyword(s):  
Stationary Distribution ◽  
Stochastic Perturbation ◽  
Pathwise Estimation ◽  
Mutualism System

scholarly journals Existence, Uniqueness and Ergodicity of Positive Solution of Mutualism System with Stochastic Perturbation

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
Chunyan Ji ◽  
Daqing Jiang ◽  
Hong Liu ◽  
Qingshan Yang
Keyword(s):  
Positive Solution ◽  
Stationary Distribution ◽  
Nonnegative Solution ◽  
Stochastic Perturbation ◽  
Ergodic Property ◽  
Mutualism System

We discuss a two-species Lotka-Volterra mutualism system with stochastic perturbation. We show that there is a unique nonnegative solution of this system. Furthermore, we investigate that there exists a stationary distribution for this system, and it has ergodic property.

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.

The stationary distribution and ergodicity of a stochastic mutualism model

2018 ◽  
Vol 68 (3) ◽  
pp. 685-690 ◽  
Author(s):  
Jingliang Lv ◽  
Sirun Liu ◽  
Heng Liu
Keyword(s):  
Stochastic Model ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Ergodic Property ◽  
Model Simulations ◽  
Analytical Results ◽  
Stationary Distribution And Ergodicity ◽  
Mutualism Model ◽  
Mutualism System

Abstract This paper is concerned with a stochastic mutualism system with toxicant substances and saturation terms. We obtain the sufficient conditions for the existence of a unique stationary distribution to the equation and it has an ergodic property. It is interesting and surprising that toxicant substances have no effect on the stationary distribution of the stochastic model. Simulations are also carried out to confirm our analytical results.

scholarly journals Extinction and Stationary Distribution of a Stochastic SIRS Epidemic Model Incorporating Media Coverage

2019 ◽  
pp. 1-19
Author(s):  
Eric N'zi ◽  
Modeste N'zi
Keyword(s):  
Numerical Simulations ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Media Coverage ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Demographic Stochasticity ◽  
Sirs Epidemic Model ◽  
The Media ◽  
Well Posed

In this paper, we include stochastic perturbation into SIRS epidemic model incorporating media coverage and study their dynamics. Our model is obtained by taking into account both for demographic stochasticity and environmental fluctuations on contact rate before alert media β1. First, we show that the model is biologically well-posed by proving the global existence, positivity and boundedness of solution . Then, sufficient conditions for the extinction of infectious diseaseis proved. We also established sufficient conditions for the existence of an ergodic stationary distribution to the model. Finally, the theoretical results are illustrated by numerical simulations; in addition we show that the media coverage can reduce the peak of infective individuals via numerical simulations.

scholarly journals The Stationary Distribution of Competitive Lotka-Volterra Population Systems with Jumps

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Zhenzhong Zhang ◽  
Jinying Tong ◽  
Jianhai Bao
Keyword(s):  
Stationary Distribution ◽  
Asymptotic Properties ◽  
Pathwise Estimation

Dynamics of Lotka-Volterra population with jumps (LVWJ) have recently been established (see Bao et al., 2011, and Bao and Yuan, 2012). They provided some useful criteria on the existence of stationary distribution and some asymptotic properties for LVWJ. However, the uniqueness of stationary distribution forn≥2and asymptotic pathwise estimationlimt→+∞⁡(1/t)∫0t‍|X(s)|pds (p>0)are still unknown for LVWJ. One of our aims in this paper is to show the uniqueness of stationary distribution and asymptotic pathwise estimation for LVWJ. Moreover, some characterizations for stationary distribution are provided.

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.

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