scholarly journals Dynamics of a single predator multiple prey model with stochastic perturbation and seasonal variation

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 535-549
Author(s):  
Hong-Wen Hui ◽  
Lin-Fei Nie
Keyword(s):  
Seasonal Variation ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Analysis Method ◽  
Ultimate Boundedness ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean ◽  
Stochastically Ultimate Boundedness ◽  
Theoretical Results

Considering various factors are stochastic rather than deterministic in the evolution of populations growth, in this paper, we propose a single predator multiple prey stochastic model with seasonal variation. By using the method of solving an explicit solution, the existence of global positive solution of this model are obtained. The method is more convenient than Lyapunov analysis method for some population models. Moreover, the stochastically ultimate boundedness are considered by using the comparison theorem of stochastic differential equation. Further, some sufficient conditions for the extinction and strong persistence in the mean of populations are discussed, respectively. In addition, by constructing some suitable Lyapunov functions, we show that this model admits at least one periodic solution. Finally, numerical simulations clearly illustrate the main theoretical results and the effects of white noise and seasonal variation for the persistence and extinction of populations.

Effects of Toxicants on a Non-Autonomous Predator-Prey Model with Random Perturbation

2015 ◽  
Vol 737 ◽  
pp. 487-490
Author(s):  
Yan Zhang ◽  
Kuan Gang Fan ◽  
Qing Yun Wang
Keyword(s):  
Random Perturbation ◽  
Stochastic Perturbation ◽  
Ultimate Boundedness ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean ◽  
Stochastically Ultimate Boundedness

A new non-autonomous predator-prey model in a polluted environment with stochastic perturbation is considered in this paper. The existence of a global positive solution and stochastically ultimate boundedness are derived. Furthermore, some sufficient and necessary criteria for extinction, non-persistence in the mean, weak persistence in the mean, strong persistence in the mean are obtained. At last, a series of numerical simulations to illustrate our mathematical findings are presented.

Dynamics of a stochastic predator–prey model with mutual interference

2014 ◽  
Vol 07 (03) ◽  
pp. 1450026 ◽  
Author(s):  
Kai Wang ◽  
Yanling Zhu
Keyword(s):  
Numerical Simulation ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Mutual Interference ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Persistence In The Mean ◽  
The Mean ◽  
Globally Positive Solution

In this paper, a stochastic predator–prey (PP) model with mutual interference is considered. Some sufficient conditions for the existence of globally positive solution, non-persistence in the mean, weak persistence in the mean, strong persistence in the mean and almost surely extinction of the the model are established. Moreover, the threshold between weak persistence in the mean and almost surely extinction of the prey is obtained. Some examples are given to show the feasibility of the results by numerical simulation. It is significant that such a model is firstly proposed with stochastic perturbation.

Stochastic dynamics of the transmission of Dengue fever virus between mosquitoes and humans

2021 ◽  
pp. 2150062
Author(s):  
Manjing Guo ◽  
Lin Hu ◽  
Lin-Fei Nie
Keyword(s):  
Dengue Fever ◽  
Stochastic Dynamics ◽  
Sufficient Conditions ◽  
Lyapunov Methods ◽  
Differential Model ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean ◽  
And Behavior ◽  
The Impact

Considering the impact of environmental white noise on the quantity and behavior of vector of disease, a stochastic differential model describing the transmission of Dengue fever between mosquitoes and humans, in this paper, is proposed. By using Lyapunov methods and Itô’s formula, we first prove the existence and uniqueness of a global positive solution for this model. Further, some sufficient conditions for the extinction and persistence in the mean of this stochastic model are obtained by using the techniques of a series of stochastic inequalities. In addition, we also discuss the existence of a unique stationary distribution which leads to the stochastic persistence of this disease. Finally, several numerical simulations are carried to illustrate the main results of this contribution.

Study on a susceptible–infected–vaccinated model with delay and proportional vaccination

2018 ◽  
Vol 11 (08) ◽  
pp. 1850102 ◽  
Author(s):  
Shuqi Gan ◽  
Fengying Wei
Keyword(s):  
Positive Solution ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Stochastic Epidemic ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean ◽  
Stochastic Epidemic Model

A susceptible–infected–vaccinated epidemic model with proportional vaccination and generalized nonlinear rate is formulated and investigated in the paper. We show that the stochastic epidemic model admits a unique and global positive solution with probability one when constructing a proper [Formula: see text]-function therewith. Then a sufficient condition that guarantees the disappearances of diseases is derived when the indicator [Formula: see text]. Further, if [Formula: see text], then we obtain that the solution is weakly permanent with probability one. We also derived the sufficient conditions of the persistence in the mean for the susceptible and infected when another indicator [Formula: see text].

scholarly journals Asymptotic Behavior of a Chemostat Model with Stochastic Perturbation on the Dilution Rate

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chaoqun Xu ◽  
Sanling Yuan ◽  
Tonghua Zhang
Keyword(s):  
Dilution Rate ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Positive Equilibrium ◽  
Deterministic System ◽  
Time Behavior ◽  
Chemostat Model ◽  
Persistence In The Mean ◽  
Long Time ◽  
The Mean

We present a stochastic simple chemostat model in which the dilution rate was influenced by white noise. The long time behavior of the system is studied. Mainly, we show how the solution spirals around the washout equilibrium and the positive equilibrium of deterministic system under different conditions. Furthermore, the sufficient conditions for persistence in the mean of the stochastic system and washout of the microorganism are obtained. Numerical simulations are carried out to support our results.

scholarly journals Stochastically Ultimate Boundedness and Global Attraction of Positive Solution for a Stochastic Competitive System

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Shengliang Guo ◽  
Zhijun Liu ◽  
Huili Xiang
Keyword(s):  
Lyapunov Function ◽  
Positive Solution ◽  
Finite Time ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Ultimate Boundedness ◽  
Competitive System ◽  
Global Attraction ◽  
Stochastically Ultimate Boundedness ◽  
Theoretical Results

A stochastic competitive system is investigated. We first show that the positive solution of the above system does not explode to infinity in a finite time, and the existence and uniqueness of positive solution are discussed. Later, sufficient conditions for the stochastically ultimate boundedness of positive solution are derived. Also, with the help of Lyapunov function, sufficient conditions for the global attraction of positive solution are established. Finally, numerical simulations are presented to justify our theoretical results.

A generalized stochastic competitive system with Ornstein–Uhlenbeck process

2020 ◽  
pp. 2150001
Author(s):  
Baodan Tian ◽  
Liu Yang ◽  
Xingzhi Chen ◽  
Yong Zhang
Keyword(s):  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Competitive System ◽  
Uhlenbeck Process ◽  
Stochastic Perturbations ◽  
Stochastic Permanence ◽  
Persistence In The Mean ◽  
Ornstein Uhlenbeck Process ◽  
Global Positive Solution ◽  
The Mean

A generalized competitive system with stochastic perturbations is proposed in this paper, in which the stochastic disturbances are described by the famous Ornstein–Uhlenbeck process. By theories of stochastic differential equations, such as comparison theorem, Itô’s integration formula, Chebyshev’s inequality, martingale’s properties, etc., the existence and the uniqueness of global positive solution of the system are obtained. Then sufficient conditions for the extinction of the species almost surely, persistence in the mean and the stochastic permanence for the system are derived, respectively. Finally, by a series of numerical examples, the feasibility and correctness of the theoretical analysis results are verified intuitively. Moreover, the effects of the intensity of the stochastic perturbations and the speed of the reverse in the Ornstein–Uhlenbeck process to the dynamical behavior of the system are also discussed.

Dynamics of a stochastic delayed avian influenza model with mutation and temporary immunity

2021 ◽  
pp. 2150029
Author(s):  
Ting Kang ◽  
Qimin Zhang
Keyword(s):  
Avian Influenza ◽  
Deterministic Model ◽  
Sufficient Conditions ◽  
Human Populations ◽  
Deterministic System ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean ◽  
White Noises ◽  
Temporary Immunity

In this paper, the dynamic behaviors are studied for a stochastic delayed avian influenza model with mutation and temporary immunity. First, we prove the existence and uniqueness of the global positive solution for the stochastic model. Second, we give two different thresholds [Formula: see text] and [Formula: see text], and further establish the sufficient conditions of extinction and persistence in the mean for the avian-only subsystem and avian-human system, respectively. Compared with the corresponding deterministic model, the thresholds affected by the white noises are smaller than the ones of the deterministic system. Finally, numerical simulations are carried out to support our theoretical results. It is concluded that the vaccination immunity period can suppress the spread of avian influenza during poultry and human populations, while prompt the spread of mutant avian influenza in human population.

scholarly journals Extinction Analysis of Stochastic Predator–Prey System with Stage Structure and Crowley–Martin Functional Response

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 252 ◽  
Author(s):  
Conghui Xu ◽  
Guojian Ren ◽  
Yongguang Yu
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Ultimate Boundedness ◽  
Predator Prey ◽  
Dynamical Behaviors ◽  
Prey System ◽  
Global Positive Solution ◽  
Stochastically Ultimate Boundedness ◽  
Stochastic Extinction

In this paper, we researched some dynamical behaviors of a stochastic predator–prey system, which is considered under the combination of Crowley–Martin functional response and stage structure. First, we obtained the existence and uniqueness of the global positive solution of the system. Then, we studied the stochastically ultimate boundedness of the solution. Furthermore, we established two sufficient conditions, which are separately given to ensure the stochastic extinction of the prey and predator populations. In the end, we carried out the numerical simulations to explain some cases.

scholarly journals Dynamics of a stochastic phytoplankton-toxic phytoplankton-zooplankton system under regime switching

2021 ◽  
Author(s):  
He Liu ◽  
Chuanjun Dai ◽  
Hengguo Yu ◽  
Qing Guo ◽  
Jianbing Li ◽  
...  
Keyword(s):  
White Noise ◽  
Regime Switching ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Aquatic Environments ◽  
Combined Effects ◽  
Toxic Phytoplankton ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean

In this paper, a stochastic phytoplankton-toxic phytoplankton-zooplankton system with Beddington-DeAngelis functional response, where both the white noise and regime switching are taken into account, is studied analytically and numerically. The aim of this research is to study the combined effects of the white noise, regime switching and toxin-producing phytoplankton (TPP) on the dynamics of the system. Firstly, the existence and uniqueness of global positive solution of the system is investigated. Then some sufficient conditions for the extinction, persistence in the mean and the existence of a unique ergidoc stationary distribution of the system are derived. Significantly, some numerical simulations are carried to verify our analytical results, and show that high intensity of white noise is harmful to the survival of plankton populations, but regime switching can balance the different survival states of plankton populations and decrease the risk of extinction. Additionally, it is found that an increase in the toxin liberation rate produced by TPP will increase the survival change of phytoplankton, while it will reduce the biomass of zooplankton. All these results may provide some insightful understanding on the dynamics of phytoplankton-zooplankton system in randomly disturbed aquatic environments.

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