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

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 an...

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Main Authors: Tingting Ma, Xinzhu Meng, Zhengbo Chang
Format: Article
Language:English
Published: Wiley 2019-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2019/5342031
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author Tingting Ma
Xinzhu Meng
Zhengbo Chang
author_facet Tingting Ma
Xinzhu Meng
Zhengbo Chang
author_sort Tingting Ma
collection DOAJ
description 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.
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institution Kabale University
issn 1076-2787
1099-0526
language English
publishDate 2019-01-01
publisher Wiley
record_format Article
series Complexity
spelling doaj-art-c0a0e331081944a1b584c9ec032e5d102025-02-03T06:11:34ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/53420315342031Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with JumpsTingting Ma0Xinzhu Meng1Zhengbo Chang2College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaWe 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.http://dx.doi.org/10.1155/2019/5342031
spellingShingle Tingting Ma
Xinzhu Meng
Zhengbo Chang
Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps
Complexity
title Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps
title_full Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps
title_fullStr Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps
title_full_unstemmed Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps
title_short Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps
title_sort dynamics and optimal harvesting control for a stochastic one predator two prey time delay system with jumps
url http://dx.doi.org/10.1155/2019/5342031
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AT xinzhumeng dynamicsandoptimalharvestingcontrolforastochasticonepredatortwopreytimedelaysystemwithjumps
AT zhengbochang dynamicsandoptimalharvestingcontrolforastochasticonepredatortwopreytimedelaysystemwithjumps