A note on the stationary distribution of a three-species food web stochastic model with generalist predator

2021 ◽  
Vol 114 ◽  
pp. 106929
Author(s):  
Qun Liu ◽  
Qingmei Chen
Keyword(s):  
Stochastic Model ◽  
Food Web ◽  
Stationary Distribution ◽  
Generalist Predator

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 The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Firas Hussean Maghool ◽  
Raid Kamel Naji
Keyword(s):  
Food Web ◽  
Evolutionary Biology ◽  
Basin Of Attraction ◽  
Growth Function ◽  
Generalist Predator ◽  
Specific Level ◽  
Predator Species ◽  
Web System ◽  
Group Defense ◽  
The Impact

The avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying the impact of prey’s fear and group defense against predation on the dynamics of the food-web model. Consequently, in this paper, a mathematical model that describes a tritrophic Leslie-Gower food-web system is formulated. Sokol-Howell type of function response is adapted to describe the predation process due to the prey’s group defensive capability. The effects of fear due to the predation process are considered in the first two levels. It is assumed that the generalist predator grows logistically using the Leslie-Gower type of growth function. All the solution properties of the model are studied. Local dynamics behaviors are investigated. The basin of attraction for each equilibrium is determined using the Lyapunov function. The conditions of persistence of the model are specified. The study of local bifurcation in the model is done. Numerical simulations are implemented to show the obtained results. It is watched that the system is wealthy in its dynamics including chaos. The fear factor works as a stabilizing factor in the system up to a specific level; otherwise, it leads to the extinction of the predator. However, increasing the prey’s group defense leads to extinction in predator species.

scholarly journals Correction: Liu, P., et al. Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity. Symmetry 2020, 12, 331

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 629
Author(s):  
Peng Liu ◽  
Xinzhu Meng ◽  
Haokun Qi
Keyword(s):  
Stochastic Model ◽  
Stationary Distribution ◽  
Threshold Analysis ◽  
Temporary Immunity

The authors wish to make the following corrections and explanations to this paper [...]

scholarly journals Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 331 ◽  
Author(s):  
Peng Liu ◽  
Xinzhu Meng ◽  
Haokun Qi
Keyword(s):  
Stochastic Model ◽  
Stationary Distribution ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Markov Semigroup ◽  
Threshold Analysis ◽  
Numerical Examples ◽  
Stochastic Properties ◽  
Symmetric Method ◽  
Temporary Immunity

In this paper, a stochastic model with relapse and temporary immunity is formulated. The main purpose of this model is to investigate the stochastic properties. For two incidence rate terms, we apply the ideas of a symmetric method to obtain the results. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the extinction and persistence of this system. Then, we investigate the existence of a stationary distribution for this model by employing the theory of an integral Markov semigroup. Finally, the numerical examples are presented to illustrate the analytical findings.

scholarly journals Intrapopulation niche partitioning in a generalist predator limits food web connectivity

Ecology ◽  
2009 ◽  
Vol 90 (8) ◽  
pp. 2263-2274 ◽  
Author(s):  
Mario Quevedo ◽  
Richard Svanbäck ◽  
Peter Eklöv
Keyword(s):  
Food Web ◽  
Niche Partitioning ◽  
Generalist Predator

A MARKOVIAN MODEL FOR COOPERATIVE INTERACTIONS IN PROTEINS

1995 ◽  
Vol 05 (06) ◽  
pp. 835-863 ◽  
Author(s):  
M. ABUNDO ◽  
L. ACCARDI ◽  
N. ROSATO
Keyword(s):  
Stochastic Model ◽  
Chemical Bond ◽  
Stationary Distribution ◽  
Cooperative Behavior ◽  
Critical Value ◽  
Markovian Model ◽  
Birth And Death Processes ◽  
Cooperative Interactions ◽  
The Mean ◽  
Two Parameters

A stochastic model for cooperative interactions in proteins is proposed. The description is based on the theory of Markov’s chains and of birth-and-death processes. Even if the model depends only on two parameters: the mean probability p and the coupling capacity∆p, it presents a surprising wealth of qualitative behaviors when the two parameters are varied. In particular we provide numerical evidence of change of concavity of the stationary distribution at a critical value of the coupling capacity ∆p. The main mathematical feature is that the probability of creating a new chemical bond depends on the total number of bonds already present in the system. In this sense, we speak of a cooperative behavior.

scholarly journals Stationary distribution of a stochastic SIRD epidemic model of Ebola with double saturated incidence rates and vaccination

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Panpan Wang ◽  
Jianwen Jia
Keyword(s):  
Stochastic Model ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Lyapunov Functions ◽  
Incidence Rates ◽  
Saturated Incidence ◽  
Global Positive Solution

Abstract In this paper, a stochastic SIRD model of Ebola with double saturated incidence rates and vaccination is considered. Firstly, the existence and uniqueness of a global positive solution are obtained. Secondly, by constructing suitable Lyapunov functions and using Khasminskii’s theory, we show that the stochastic model has a unique stationary distribution. Moreover, the extinction of the disease is also analyzed. Finally, numerical simulations are carried out to portray the analytical results.

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