scholarly journals Analysis of a Stochastic Competitive Model with Distributed Time Delays and Jumps in a Polluted Environment

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Taolin Zhang ◽  
Yuanfu Shao ◽  
Xiaowan She
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Time Delays ◽  
Polluted Environment ◽  
Persistence In Mean ◽  
Distributed Time Delays ◽  
Competitive Model ◽  
Stability In Distribution ◽  
Lévy Jumps ◽  
Theoretical Results

In this paper, a stochastic competitive model with distributed time delays and Lévy jumps is formulated. With or without a polluted environment, the model is denoted by (M) or (M0), respectively. The existence of positive solution, persistence in mean, and extinction of species for (M) and (M0) are both studied. The sufficient criteria of stability in distribution for model (M) is obtained. Finally, some numerical simulations are given to illustrate our theoretical results.

Dynamics of a stochastic three-species competitive model with Lévy jumps

2018 ◽  
Vol 11 (05) ◽  
pp. 1850075
Author(s):  
Yongxin Gao ◽  
Shiquan Tian
Keyword(s):  
Numerical Simulations ◽  
Critical Value ◽  
Persistence In The Mean ◽  
Competitive Model ◽  
Stability In Distribution ◽  
Parameters Analysis ◽  
The Mean ◽  
Lévy Jumps ◽  
White Noises ◽  
Theoretical Results

This paper is concerned with a three-species competitive model with both white noises and Lévy noises. We first carry out the almost complete parameters analysis for the model and establish the critical value between persistence in the mean and extinction for each species. The sufficient criteria for stability in distribution of solutions are obtained. Finally, numerical simulations are carried out to verify the theoretical results.

scholarly journals Optimal harvesting strategies of a stochastic competitive model with S-type distributed time delays and Lévy jumps

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hong Qiu ◽  
Wenmin Deng ◽  
Mingqi Xiang
Keyword(s):  
Time Delays ◽  
Sufficient Conditions ◽  
Volterra Model ◽  
Optimal Harvesting ◽  
Ergodic Method ◽  
Technical Assumption ◽  
Distributed Time Delays ◽  
Competitive Model ◽  
The Stability ◽  
Lévy Jumps

AbstractThe aim of this paper is to investigate the optimal harvesting strategies of a stochastic competitive Lotka–Volterra model with S-type distributed time delays and Lévy jumps by using ergodic method. Firstly, the sufficient conditions for extinction and stable in the time average of each species are established under some suitable assumptions. Secondly, under a technical assumption, the stability in distribution of this model is proved. Then the sufficient and necessary criteria for the existence of optimal harvesting policy are established under the condition that all species are persistent. Moreover, the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are given.

scholarly journals Dynamics and optimal harvesting of a stochastic predator-prey system with regime switching, S-type distributed time delays and Lévy jumps

2021 ◽  
Vol 7 (3) ◽  
pp. 4068-4093
Author(s):  
Yuanfu Shao ◽  
Keyword(s):  
Regime Switching ◽  
Time Delays ◽  
Optimal Harvesting ◽  
Comparison Theory ◽  
Predator Prey ◽  
Prey System ◽  
Persistence In The Mean ◽  
Distributed Time Delays ◽  
Stability In Distribution ◽  
Lévy Jumps

<abstract><p>This work is concerned with a stochastic predator-prey system with S-type distributed time delays, regime switching and Lévy jumps. By use of the stochastic differential comparison theory and some inequality techniques, we study the extinction and persistence in the mean for each species, asymptotic stability in distribution and the optimal harvesting effort of the model. Then we present some simulation examples to illustrate the theoretical results and explore the effects of regime switching, distributed time delays and Lévy jumps on the dynamical behaviors, respectively.</p></abstract>

scholarly journals Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Tingting Ma ◽  
Xinzhu Meng ◽  
Zhengbo Chang
Keyword(s):  
Differential Equations ◽  
Time Delays ◽  
Hessian Matrix ◽  
Sufficient Conditions ◽  
Delay System ◽  
Optimal Harvesting ◽  
Time Delay System ◽  
Stability In Distribution ◽  
Lévy Jumps ◽  
Theoretical Results

We consider a stochastic one-predator-two-prey harvesting model with time delays and Lévy jumps in this paper. Using the comparison theorem of stochastic differential equations and asymptotic approaches, sufficient conditions for persistence in mean and extinction of three species are derived. By analyzing the asymptotic invariant distribution, we study the variation of the persistent level of a population. Then we obtain the conditions of global attractivity and stability in distribution. Furthermore, making use of Hessian matrix method and optimal harvesting theory of differential equations, the explicit forms of optimal harvesting effort and maximum expectation of sustainable yield are obtained. Some numerical simulations are given to illustrate the theoretical results.

scholarly journals Coexistence for a kind of stochastic three-species competitive models

2019 ◽  
Vol 17 (1) ◽  
pp. 1203-1219
Author(s):  
Nantian Huang ◽  
Jiabing Huang ◽  
Yuming Wei ◽  
Yongjian Liu
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Convergence In Distribution ◽  
Threshold Values ◽  
Linear Diffusion ◽  
Ecological Balance ◽  
Non Linear ◽  
Competitive Model ◽  
Theoretical Results

Abstract The coexistence of species sustains the ecological balance in nature. This paper focuses on sufficient conditions for the coexistence of a three-species stochastic competitive model, where the model has non-linear diffusion parts. Three values λ3z, λ3x and λ3y are introduced and calculated from the coefficients, which can be considered as threshold values. Moreover, convergence in distribution of the positive solution of the model is also addressed. A few numerical simulations are carried out to illustrate the theoretical results.

scholarly journals Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Guodong Liu ◽  
Xiaohong Wang ◽  
Xinzhu Meng ◽  
Shujing Gao
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Persistence In Mean ◽  
Predator Prey Model ◽  
Prey System ◽  
Delay Differential ◽  
Lévy Jumps

In this paper, we explore an impulsive stochastic infected predator-prey system with Lévy jumps and delays. The main aim of this paper is to investigate the effects of time delays and impulse stochastic interference on dynamics of the predator-prey model. First, we prove some properties of the subsystem of the system. Second, in view of comparison theorem and limit superior theory, we obtain the sufficient conditions for the extinction of this system. Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). Finally, we carry out some simulations to verify our main results and explain the biological implications.

scholarly journals A Discrete Model for HIV Infection with Distributed Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Brahim EL Boukari ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Hiv Infection ◽  
Global Stability ◽  
Time Delays ◽  
Discrete Model ◽  
Distributed Delay ◽  
Continuous Model ◽  
Distributed Time Delays ◽  
A Cell ◽  
The Times ◽  
Theoretical Results

We give a consistent discretization of a continuous model of HIV infection, with distributed time delays to express the lag between the times when the virus enters a cell and when the cell becomes infected. The global stability of the steady states of the model is determined and numerical simulations are presented to illustrate our theoretical results.

Dynamic of a stochastic delayed one-predator two-prey model with Lévy jumps in polluted environments

2020 ◽  
pp. 2150002
Author(s):  
Yongxin Gao ◽  
Nana Wang ◽  
Shiquan Tian
Keyword(s):  
Numerical Simulations ◽  
Nonnegative Solution ◽  
Prey Model ◽  
Time Average ◽  
Lévy Jumps ◽  
Theoretical Results

This paper is concerned with a stochastic delayed one-predator two-prey model with Lévy jumps in polluted environments. First, under some simple assumptions, we prove that there exists a unique global nonnegative solution which is permanent in time average. Moreover, sufficient criteria for the extinction of each species are obtained. Finally, we carry out some numerical simulations to verify the theoretical results.

Dynamics of a stochastic rabies epidemic model with markovian switching

2021 ◽  
pp. 2150032
Author(s):  
Hao Peng ◽  
Xinhong Zhang ◽  
Daqing Jiang
Keyword(s):  
Lyapunov Function ◽  
White Noise ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Telegraph Noise ◽  
Global Positive Solution ◽  
Theoretical Results

In this paper, we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise. First, we prove the existence of the unique global positive solution. Second, by constructing an appropriate Lyapunov function, we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for the extinction of diseases. Finally, numerical simulations are introduced to illustrate our theoretical results.

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