Global Attractivity of an Integrodifferential Model of Mutualism - Xiangdong Xie; Fengde Chen; Kun Yang; Yalong Xue (Abstract and Applied Analysis)
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.