Global Attractivity of an Integrodifferential Model of Mutualism

作者：Xie, Xiangdong^*; Chen, Fengde; Yang, Kun; Xue, Yalong

来源：Abstract and Applied Analysis, 2014, 2014: 928726.

DOI：10.1155/2014/928726

• VOLTERRA COOPERATIVE SYSTEMS
• POSITIVE PERIODIC-SOLUTIONS
• CONTINUOUS-TIME DELAYS
• FEEDBACK CONTROLS
• FACULTATIVE MUTUALISM
• PERMANENCE

Sufficient conditions are obtained for the global attractivity of the following integrodifferential model of mutualism dN(1)(t)/dt = r(1)N(1)(t)[((K-1 + alpha(1) integral(infinity)(0) J(2)(s)N-2(t - s)ds)/(1 + integral(infinity)(0) J(2)(s)N-2(t - s)ds - N-1(t), dN(2)(t)/dt = r(2)N(2)(t)[((K-2 + alpha(2) integral(infinity)(0) J(1)(s)N-1(t - s)ds)/(1 + integral(infinity)(0) J(1)(s)N-1(t - s)ds)) - N-2(t)], where r(i), K-i, and alpha(i), i = 1,2, are all positive constants. Consider alpha(i) > K-i, i = 1,2. Consider J(1) is an element of C([0, +infinity), [0, +infinity)) and integral(infinity)(0) J(i)(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.

• 出版日期2014
• 单位宁德师范学院; 福州大学