Extinction Analysis of Stochastic Predator–Prey System with Stage Structure and Crowley–Martin Functional Response
In this paper, we researched some dynamical behaviors of a stochastic predator–prey system, which is considered under the combination of Crowley–Martin functional response and stage structure. First, we obtained the existence and uniqueness of the global positive solution of the...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-03-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/21/3/252 |
| _version_ | 1811184069273190400 |
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| author | Conghui Xu Guojian Ren Yongguang Yu |
| author_facet | Conghui Xu Guojian Ren Yongguang Yu |
| author_sort | Conghui Xu |
| collection | DOAJ |
| description | In this paper, we researched some dynamical behaviors of a stochastic predator–prey system, which is considered under the combination of Crowley–Martin functional response and stage structure. First, we obtained the existence and uniqueness of the global positive solution of the system. Then, we studied the stochastically ultimate boundedness of the solution. Furthermore, we established two sufficient conditions, which are separately given to ensure the stochastic extinction of the prey and predator populations. In the end, we carried out the numerical simulations to explain some cases. |
| first_indexed | 2024-04-11T13:08:07Z |
| format | Article |
| id | doaj.art-516e9e846e6a4270bb263d2842ff98f7 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T13:08:07Z |
| publishDate | 2019-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-516e9e846e6a4270bb263d2842ff98f72022-12-22T04:22:40ZengMDPI AGEntropy1099-43002019-03-0121325210.3390/e21030252e21030252Extinction Analysis of Stochastic Predator–Prey System with Stage Structure and Crowley–Martin Functional ResponseConghui Xu0Guojian Ren1Yongguang Yu2School of Science, Beijing Jiaotong University, Beijing 100044, ChinaSchool of Science, Beijing Jiaotong University, Beijing 100044, ChinaSchool of Science, Beijing Jiaotong University, Beijing 100044, ChinaIn this paper, we researched some dynamical behaviors of a stochastic predator–prey system, which is considered under the combination of Crowley–Martin functional response and stage structure. First, we obtained the existence and uniqueness of the global positive solution of the system. Then, we studied the stochastically ultimate boundedness of the solution. Furthermore, we established two sufficient conditions, which are separately given to ensure the stochastic extinction of the prey and predator populations. In the end, we carried out the numerical simulations to explain some cases.http://www.mdpi.com/1099-4300/21/3/252predator–prey systemstochastically ultimate boundednessstochastic extinctionBrownian motionCrowley–Martin functional response |
| spellingShingle | Conghui Xu Guojian Ren Yongguang Yu Extinction Analysis of Stochastic Predator–Prey System with Stage Structure and Crowley–Martin Functional Response Entropy predator–prey system stochastically ultimate boundedness stochastic extinction Brownian motion Crowley–Martin functional response |
| title | Extinction Analysis of Stochastic Predator–Prey System with Stage Structure and Crowley–Martin Functional Response |
| title_full | Extinction Analysis of Stochastic Predator–Prey System with Stage Structure and Crowley–Martin Functional Response |
| title_fullStr | Extinction Analysis of Stochastic Predator–Prey System with Stage Structure and Crowley–Martin Functional Response |
| title_full_unstemmed | Extinction Analysis of Stochastic Predator–Prey System with Stage Structure and Crowley–Martin Functional Response |
| title_short | Extinction Analysis of Stochastic Predator–Prey System with Stage Structure and Crowley–Martin Functional Response |
| title_sort | extinction analysis of stochastic predator prey system with stage structure and crowley martin functional response |
| topic | predator–prey system stochastically ultimate boundedness stochastic extinction Brownian motion Crowley–Martin functional response |
| url | http://www.mdpi.com/1099-4300/21/3/252 |
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