Dynamical Behavior of a Stochastic Food-Chain System with Beddington-DeAngelis Functional Response
We investigate a stochastic Food-Chain System dx(t)=[r1(t)-a11(t)x-(a12(t)y/(1+β1(t)x+γ1(t)y))]xdt+σ1(t)xdB1(t), dy(t)=[r2(t)-a21(t)y+(a22(t)x/(1+β1(t)x+γ1(t)y))-(a23(t)z/(1+β2(t)y+γ2(t)z))]ydt+σ2(t)ydB2(t), dz(t)=[-r3(t)+(a31(t)y/(1+β2(t)y+γ2(t)z))-a32(t)z]zdt+σ3(t)zdB3(t), where Bi(t), i = 1,2,3,...
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| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/426702 |
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| author | Yanming Ge Zigen Song |
| author_facet | Yanming Ge Zigen Song |
| author_sort | Yanming Ge |
| collection | DOAJ |
| description | We investigate a stochastic Food-Chain System dx(t)=[r1(t)-a11(t)x-(a12(t)y/(1+β1(t)x+γ1(t)y))]xdt+σ1(t)xdB1(t), dy(t)=[r2(t)-a21(t)y+(a22(t)x/(1+β1(t)x+γ1(t)y))-(a23(t)z/(1+β2(t)y+γ2(t)z))]ydt+σ2(t)ydB2(t), dz(t)=[-r3(t)+(a31(t)y/(1+β2(t)y+γ2(t)z))-a32(t)z]zdt+σ3(t)zdB3(t), where Bi(t), i = 1,2,3, is a standard Brownian motion. Firstly, the existence, the uniqueness, and the positivity of the solution are proved. Secondly, the stochastically ultimate boundedness of the system is investigated. Thirdly, the boundedness of moments and upper-growth rate of the solution are obtained. Then the global attractivity of the system is discussed. Finally, the main results are illustrated by several examples. |
| format | Article |
| id | doaj-art-10ebca1f2f0d4b89923c2191e73a985c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-10ebca1f2f0d4b89923c2191e73a985c2025-08-20T03:55:45ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/426702426702Dynamical Behavior of a Stochastic Food-Chain System with Beddington-DeAngelis Functional ResponseYanming Ge0Zigen Song1College of Information Technology, Shanghai Ocean University, Shanghai 201306, ChinaCollege of Information Technology, Shanghai Ocean University, Shanghai 201306, ChinaWe investigate a stochastic Food-Chain System dx(t)=[r1(t)-a11(t)x-(a12(t)y/(1+β1(t)x+γ1(t)y))]xdt+σ1(t)xdB1(t), dy(t)=[r2(t)-a21(t)y+(a22(t)x/(1+β1(t)x+γ1(t)y))-(a23(t)z/(1+β2(t)y+γ2(t)z))]ydt+σ2(t)ydB2(t), dz(t)=[-r3(t)+(a31(t)y/(1+β2(t)y+γ2(t)z))-a32(t)z]zdt+σ3(t)zdB3(t), where Bi(t), i = 1,2,3, is a standard Brownian motion. Firstly, the existence, the uniqueness, and the positivity of the solution are proved. Secondly, the stochastically ultimate boundedness of the system is investigated. Thirdly, the boundedness of moments and upper-growth rate of the solution are obtained. Then the global attractivity of the system is discussed. Finally, the main results are illustrated by several examples.http://dx.doi.org/10.1155/2014/426702 |
| spellingShingle | Yanming Ge Zigen Song Dynamical Behavior of a Stochastic Food-Chain System with Beddington-DeAngelis Functional Response Abstract and Applied Analysis |
| title | Dynamical Behavior of a Stochastic Food-Chain System with Beddington-DeAngelis Functional Response |
| title_full | Dynamical Behavior of a Stochastic Food-Chain System with Beddington-DeAngelis Functional Response |
| title_fullStr | Dynamical Behavior of a Stochastic Food-Chain System with Beddington-DeAngelis Functional Response |
| title_full_unstemmed | Dynamical Behavior of a Stochastic Food-Chain System with Beddington-DeAngelis Functional Response |
| title_short | Dynamical Behavior of a Stochastic Food-Chain System with Beddington-DeAngelis Functional Response |
| title_sort | dynamical behavior of a stochastic food chain system with beddington deangelis functional response |
| url | http://dx.doi.org/10.1155/2014/426702 |
| work_keys_str_mv | AT yanmingge dynamicalbehaviorofastochasticfoodchainsystemwithbeddingtondeangelisfunctionalresponse AT zigensong dynamicalbehaviorofastochasticfoodchainsystemwithbeddingtondeangelisfunctionalresponse |