Existence of periodic solutions for a periodic mutualism model on time scales

By using Mawhin’s continuation theorem of coincidence degree theory, sufficient criteria are obtained for the existence of periodic solutions of the mutualism model ⎧⎪⎪⎪⎨ ⎪⎪⎪⎩ x (t) = r1(t) K1(t) +α1(t) exp{y(t −τ2(t, y(t)))} 1+exp{y(t − τ2(t, y(t)))} − exp x t − σ1 t,x(t) , y (t) = r2(t) K2(t) +α2(t) exp{x(t −τ1(t, x(t)))} 1+exp{x(t − τ1(t, x(t)))} − exp y t − σ2 t,y(t) , where ri,Ki,αi ∈ C(T,R + ), αi > Ki , i = 1, 2, τi,σi ∈ C(T × R,T + ), i = 1, 2, ri , Ki , αi , τi , σi (i = 1, 2) are functions of period ω>0. © 2008 Elsevier Inc. All rights reserved