scholarly journals Dynamical Analysis and Optimal Harvesting Strategy for a Stochastic Delayed Predator-Prey Competitive System with Lévy Jumps

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Guodong Liu ◽  
Kaiyuan Liu ◽  
Xinzhu Meng
Keyword(s):  
Hessian Matrix ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Optimal Harvesting ◽  
Competitive System ◽  
Stochastic Delay ◽  
Predator Prey ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Lévy Jumps

This paper develops a theoretical framework to investigate optimal harvesting control for stochastic delay differential systems. We first propose a novel stochastic two-predator and one-prey competitive system subject to time delays and Lévy jumps. Then we obtain sufficient conditions for persistence in mean and extinction of three species by using the stochastic qualitative analysis method. Finally, the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY) are derived from Hessian matrix method and optimal harvesting theory of delay differential equations. Moreover, some numerical simulations are given 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 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 Boundedness of Stochastic Delay Differential Systems with Impulsive Control and Impulsive Disturbance

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Liming Wang ◽  
Baoqing Yang ◽  
Xiaohua Ding ◽  
Kai-Ning Wu
Keyword(s):  
Stochastic Analysis ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Stochastic Delay ◽  
Analysis Techniques ◽  
Moment Boundedness ◽  
Delay Differential System ◽  
Delay Differential Systems ◽  
Delay Differential

This paper considers thep-moment boundedness of nonlinear impulsive stochastic delay differential systems (ISDDSs). Using the Lyapunov-Razumikhin method and stochastic analysis techniques, we obtain sufficient conditions which guarantee thep-moment boundedness of ISDDSs. Two cases are considered, one is that the stochastic delay differential system (SDDS) may not be bounded, and how an impulsive strategy should be taken to make the SDDS be bounded. The other is that the SDDS is bounded, and an impulsive disturbance appears in this SDDS, then what restrictions on the impulsive disturbance should be adopted to maintain the boundedness of the SDDS. Our results provide sufficient criteria for these two cases. At last, two examples are given to illustrate the correctness of our results.

scholarly journals On a predator-prey system interaction under fluctuating water level with nonselective harvesting

2020 ◽  
Vol 18 (1) ◽  
pp. 458-475
Author(s):  
Na Zhang ◽  
Yonggui Kao ◽  
Fengde Chen ◽  
Binfeng Xie ◽  
Shiyu Li
Keyword(s):  
Water Level ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Model Interaction ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fluctuating Water Level

Abstract A predator-prey model interaction under fluctuating water level with non-selective harvesting is proposed and studied in this paper. Sufficient conditions for the permanence of two populations and the extinction of predator population are provided. The non-negative equilibrium points are given, and their stability is studied by using the Jacobian matrix. By constructing a suitable Lyapunov function, sufficient conditions that ensure the global stability of the positive equilibrium are obtained. The bionomic equilibrium and the optimal harvesting policy are also presented. Numerical simulations are carried out to show the feasibility of the main 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.

Harvesting Analysis of a Predator-Prey System with Functional Response

2013 ◽  
Vol 805-806 ◽  
pp. 1957-1961
Author(s):  
Ting Wu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Predator Prey ◽  
Optimal Harvesting Policy ◽  
Prey System ◽  
The Stability ◽  
Maximal Principle

In this paper, a predator-prey system with functional response is studied,and a set of sufficient conditions are obtained for the stability of equilibrium point of the system. Moreover, optimal harvesting policy is obtained by using the maximal principle,and numerical simulation is applied to illustrate the correctness.

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