Global dynamics in a stochastic three species food-chain model with harvesting and distributed delays
Abstract This paper proposes a stochastic three species food-chain model with harvesting and distributed delays. Some criteria for the global dynamics of all positive solutions, including the existence of global positive solutions, stochastic boundedness, extinction, global asymptotic stability in t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-05-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2122-4 |
| _version_ | 1828304642539257856 |
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| author | Nafeisha Tuerxun Zhidong Teng Ahmadjan Muhammadhaji |
| author_facet | Nafeisha Tuerxun Zhidong Teng Ahmadjan Muhammadhaji |
| author_sort | Nafeisha Tuerxun |
| collection | DOAJ |
| description | Abstract This paper proposes a stochastic three species food-chain model with harvesting and distributed delays. Some criteria for the global dynamics of all positive solutions, including the existence of global positive solutions, stochastic boundedness, extinction, global asymptotic stability in the mean, and the probability distribution, are established by using the stochastic integral inequalities, Lyapunov function method, and the inequality estimation technique. Furthermore, the effects of harvesting are discussed, the optimal harvesting strategy and the maximum of expectation of sustainable yield (MESY for short) are obtained. Finally, numerical examples are carried out to illustrate our main results. |
| first_indexed | 2024-04-13T14:14:04Z |
| format | Article |
| id | doaj.art-4bd35ac5465044919d0442aae64fba74 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-04-13T14:14:04Z |
| publishDate | 2019-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-4bd35ac5465044919d0442aae64fba742022-12-22T02:43:41ZengSpringerOpenAdvances in Difference Equations1687-18472019-05-012019113010.1186/s13662-019-2122-4Global dynamics in a stochastic three species food-chain model with harvesting and distributed delaysNafeisha Tuerxun0Zhidong Teng1Ahmadjan Muhammadhaji2College of Mathematics and System Sciences, Xinjiang UniversityCollege of Mathematics and System Sciences, Xinjiang UniversityCollege of Mathematics and System Sciences, Xinjiang UniversityAbstract This paper proposes a stochastic three species food-chain model with harvesting and distributed delays. Some criteria for the global dynamics of all positive solutions, including the existence of global positive solutions, stochastic boundedness, extinction, global asymptotic stability in the mean, and the probability distribution, are established by using the stochastic integral inequalities, Lyapunov function method, and the inequality estimation technique. Furthermore, the effects of harvesting are discussed, the optimal harvesting strategy and the maximum of expectation of sustainable yield (MESY for short) are obtained. Finally, numerical examples are carried out to illustrate our main results.http://link.springer.com/article/10.1186/s13662-019-2122-4Stochastic food-chain modelDistributed delayInequality estimationExtinctionGlobal stabilityHarvesting |
| spellingShingle | Nafeisha Tuerxun Zhidong Teng Ahmadjan Muhammadhaji Global dynamics in a stochastic three species food-chain model with harvesting and distributed delays Advances in Difference Equations Stochastic food-chain model Distributed delay Inequality estimation Extinction Global stability Harvesting |
| title | Global dynamics in a stochastic three species food-chain model with harvesting and distributed delays |
| title_full | Global dynamics in a stochastic three species food-chain model with harvesting and distributed delays |
| title_fullStr | Global dynamics in a stochastic three species food-chain model with harvesting and distributed delays |
| title_full_unstemmed | Global dynamics in a stochastic three species food-chain model with harvesting and distributed delays |
| title_short | Global dynamics in a stochastic three species food-chain model with harvesting and distributed delays |
| title_sort | global dynamics in a stochastic three species food chain model with harvesting and distributed delays |
| topic | Stochastic food-chain model Distributed delay Inequality estimation Extinction Global stability Harvesting |
| url | http://link.springer.com/article/10.1186/s13662-019-2122-4 |
| work_keys_str_mv | AT nafeishatuerxun globaldynamicsinastochasticthreespeciesfoodchainmodelwithharvestinganddistributeddelays AT zhidongteng globaldynamicsinastochasticthreespeciesfoodchainmodelwithharvestinganddistributeddelays AT ahmadjanmuhammadhaji globaldynamicsinastochasticthreespeciesfoodchainmodelwithharvestinganddistributeddelays |