The Complex Dynamics of a Stochastic Predator-Prey Model
A modified stochastic ratio-dependent Leslie-Gower predator-prey model is formulated and analyzed. For the deterministic model, we focus on the existence of equilibria, local, and global stability; for the stochastic model, by applying Itô formula and constructing Lyapunov functions, some qualitativ...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/401031 |
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| _version_ | 1849682974806638592 |
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| author | Xixi Wang Huilin Huang Yongli Cai Weiming Wang |
| author_facet | Xixi Wang Huilin Huang Yongli Cai Weiming Wang |
| author_sort | Xixi Wang |
| collection | DOAJ |
| description | A modified stochastic ratio-dependent Leslie-Gower predator-prey model is
formulated and analyzed. For the deterministic model, we focus on the existence of equilibria,
local, and global stability; for the stochastic model, by applying Itô formula and constructing
Lyapunov functions, some qualitative properties are given, such as the existence of global positive
solutions, stochastic boundedness, and the global asymptotic stability. Based on these
results, we perform a series of numerical simulations and make a comparative analysis of the
stability of the model system within deterministic and stochastic environments. |
| format | Article |
| id | doaj-art-d1c3b07a154f4533a7c6847018b1462d |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d1c3b07a154f4533a7c6847018b1462d2025-08-20T03:24:02ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/401031401031The Complex Dynamics of a Stochastic Predator-Prey ModelXixi Wang0Huilin Huang1Yongli Cai2Weiming Wang3College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaSchool of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, ChinaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaA modified stochastic ratio-dependent Leslie-Gower predator-prey model is formulated and analyzed. For the deterministic model, we focus on the existence of equilibria, local, and global stability; for the stochastic model, by applying Itô formula and constructing Lyapunov functions, some qualitative properties are given, such as the existence of global positive solutions, stochastic boundedness, and the global asymptotic stability. Based on these results, we perform a series of numerical simulations and make a comparative analysis of the stability of the model system within deterministic and stochastic environments.http://dx.doi.org/10.1155/2012/401031 |
| spellingShingle | Xixi Wang Huilin Huang Yongli Cai Weiming Wang The Complex Dynamics of a Stochastic Predator-Prey Model Abstract and Applied Analysis |
| title | The Complex Dynamics of a Stochastic Predator-Prey Model |
| title_full | The Complex Dynamics of a Stochastic Predator-Prey Model |
| title_fullStr | The Complex Dynamics of a Stochastic Predator-Prey Model |
| title_full_unstemmed | The Complex Dynamics of a Stochastic Predator-Prey Model |
| title_short | The Complex Dynamics of a Stochastic Predator-Prey Model |
| title_sort | complex dynamics of a stochastic predator prey model |
| url | http://dx.doi.org/10.1155/2012/401031 |
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