Positive periodic solutions for an integrodifferential model of mutualism

Sufficient conditions are obtained for the existence of positive periodic solutions of the following integrodifferential model of mutualism: dN(1)(t)/dt = r(1)(t)N-1(t) [K-1(t) + alpha (1)(t) integral (infinity)(0) J(2)(s)N-2(t - s)ds/1 + integral (infinity)(0) J(2)N(2)(t - s)ds - N-1(t - sigma (1)(t))], dN(2)a(t)/dt = r(2)r(t)N-2(t) [K-2(t) + alpha (2)(t) 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 - sigma (2)(t))], where tau (i), K-i, alpha (i), sigma (i), i = 1,2 are positive continuous omega -periodic functions, alpha (i) > K-i, i = 1,2, J(i) is an element of C([0, infinity], [0, infinity]), and integral (infinity)(0) J(i)(s) ds = 1, i = 1, 2. (C) 2001 Elsevier Science Ltd. All rights reserved.