Global Attractivity of an Integrodifferential Model of Mutualism
Sufficient conditions are obtained for the global attractivity of the following integrodifferential model of mutualism: dN1(t)/dt=r1N1(t)[((K1+α1∫0∞J2(s)N2(t-s)ds)/(1+∫0∞J2(s)N2(t-s)ds))-N1(t)], dN2(t)/dt=r2N2(t)[((K2+α2∫0∞J1(s)N1(t-s)ds)/(1+∫0∞J1(s)N1(t-s)ds))-N2(t)], where ri,Ki, and αi, i=1,2...
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| Format: | Article |
| 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/10.1155/2014/928726 |
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| author | Xiangdong Xie Fengde Chen Kun Yang Yalong Xue |
| author_facet | Xiangdong Xie Fengde Chen Kun Yang Yalong Xue |
| author_sort | Xiangdong Xie |
| collection | DOAJ |
| description | Sufficient conditions are obtained for the global attractivity of the following integrodifferential model of mutualism: dN1(t)/dt=r1N1(t)[((K1+α1∫0∞J2(s)N2(t-s)ds)/(1+∫0∞J2(s)N2(t-s)ds))-N1(t)], dN2(t)/dt=r2N2(t)[((K2+α2∫0∞J1(s)N1(t-s)ds)/(1+∫0∞J1(s)N1(t-s)ds))-N2(t)], where ri,Ki, and αi, i=1,2, are all positive constants. Consider αi>Ki, i=1,2. Consider Ji∈C([0,+∞),[0,+∞)) and ∫0∞Ji(s)ds=1, i=1,2. Our result shows that conditions which ensure the permanence of the system are enough to ensure the global stability of the system. The result not only improves but also complements some existing ones. |
| format | Article |
| id | doaj-art-c9ffad0cc00145bdb9b015565f457617 |
| 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-c9ffad0cc00145bdb9b015565f4576172025-02-03T01:26:10ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/928726928726Global Attractivity of an Integrodifferential Model of MutualismXiangdong Xie0Fengde Chen1Kun Yang2Yalong Xue3Department of Mathematics, Ningde Normal University, Fujian 352100, ChinaDepartment of Mathematics, Ningde Normal University, Fujian 352100, ChinaCollege of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350116, ChinaCollege of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350116, ChinaSufficient conditions are obtained for the global attractivity of the following integrodifferential model of mutualism: dN1(t)/dt=r1N1(t)[((K1+α1∫0∞J2(s)N2(t-s)ds)/(1+∫0∞J2(s)N2(t-s)ds))-N1(t)], dN2(t)/dt=r2N2(t)[((K2+α2∫0∞J1(s)N1(t-s)ds)/(1+∫0∞J1(s)N1(t-s)ds))-N2(t)], where ri,Ki, and αi, i=1,2, are all positive constants. Consider αi>Ki, i=1,2. Consider Ji∈C([0,+∞),[0,+∞)) and ∫0∞Ji(s)ds=1, i=1,2. Our result shows that conditions which ensure the permanence of the system are enough to ensure the global stability of the system. The result not only improves but also complements some existing ones.http://dx.doi.org/10.1155/2014/928726 |
| spellingShingle | Xiangdong Xie Fengde Chen Kun Yang Yalong Xue Global Attractivity of an Integrodifferential Model of Mutualism Abstract and Applied Analysis |
| title | Global Attractivity of an Integrodifferential Model of Mutualism |
| title_full | Global Attractivity of an Integrodifferential Model of Mutualism |
| title_fullStr | Global Attractivity of an Integrodifferential Model of Mutualism |
| title_full_unstemmed | Global Attractivity of an Integrodifferential Model of Mutualism |
| title_short | Global Attractivity of an Integrodifferential Model of Mutualism |
| title_sort | global attractivity of an integrodifferential model of mutualism |
| url | http://dx.doi.org/10.1155/2014/928726 |
| work_keys_str_mv | AT xiangdongxie globalattractivityofanintegrodifferentialmodelofmutualism AT fengdechen globalattractivityofanintegrodifferentialmodelofmutualism AT kunyang globalattractivityofanintegrodifferentialmodelofmutualism AT yalongxue globalattractivityofanintegrodifferentialmodelofmutualism |