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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Wiley
2019-01-01
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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. |
format | Article |
id | doaj-art-c0a0e331081944a1b584c9ec032e5d10 |
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 |
work_keys_str_mv | AT tingtingma dynamicsandoptimalharvestingcontrolforastochasticonepredatortwopreytimedelaysystemwithjumps AT xinzhumeng dynamicsandoptimalharvestingcontrolforastochasticonepredatortwopreytimedelaysystemwithjumps AT zhengbochang dynamicsandoptimalharvestingcontrolforastochasticonepredatortwopreytimedelaysystemwithjumps |