Dynamical Analysis of a Stochastic Predator-Prey Model with an Allee Effect
We present and analyze a modified Holling type-II predator-prey model that includes some important factors such as Allee effect, density-dependence, and environmental noise. By constructing suitable Lyapunov functions and applying Itô formula, some qualitative properties are given, such as the exist...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/340980 |
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| _version_ | 1832568379565670400 |
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| author | Feng Rao |
| author_facet | Feng Rao |
| author_sort | Feng Rao |
| collection | DOAJ |
| description | We present and analyze a modified Holling type-II
predator-prey model that includes some important factors such as
Allee effect, density-dependence, and environmental noise. By
constructing suitable Lyapunov functions and applying Itô
formula, some qualitative properties are given, such as the
existence of global positive solutions, stochastic boundedness, and
the global asymptotic stability. A series of numerical simulations
to illustrate these mathematical findings are presented. |
| format | Article |
| id | doaj-art-a2219023ec79484f9f1b855397080f48 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a2219023ec79484f9f1b855397080f482025-02-03T00:59:13ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/340980340980Dynamical Analysis of a Stochastic Predator-Prey Model with an Allee EffectFeng Rao0College of Sciences, Nanjing University of Technology, Nanjing 211816, ChinaWe present and analyze a modified Holling type-II predator-prey model that includes some important factors such as Allee effect, density-dependence, and environmental noise. By constructing suitable Lyapunov functions and applying Itô formula, some qualitative properties are given, such as the existence of global positive solutions, stochastic boundedness, and the global asymptotic stability. A series of numerical simulations to illustrate these mathematical findings are presented.http://dx.doi.org/10.1155/2013/340980 |
| spellingShingle | Feng Rao Dynamical Analysis of a Stochastic Predator-Prey Model with an Allee Effect Abstract and Applied Analysis |
| title | Dynamical Analysis of a Stochastic Predator-Prey Model with an Allee Effect |
| title_full | Dynamical Analysis of a Stochastic Predator-Prey Model with an Allee Effect |
| title_fullStr | Dynamical Analysis of a Stochastic Predator-Prey Model with an Allee Effect |
| title_full_unstemmed | Dynamical Analysis of a Stochastic Predator-Prey Model with an Allee Effect |
| title_short | Dynamical Analysis of a Stochastic Predator-Prey Model with an Allee Effect |
| title_sort | dynamical analysis of a stochastic predator prey model with an allee effect |
| url | http://dx.doi.org/10.1155/2013/340980 |
| work_keys_str_mv | AT fengrao dynamicalanalysisofastochasticpredatorpreymodelwithanalleeeffect |