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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |