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{xΔ(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)))}],yΔ(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+)ri,Ki,αi∈C(T,R+), αi>Kiαi>Ki, i=1,2i=1,2, τi,σi∈C(T×R,T+)τi,σi∈C(T×R,T+), i=1,2i=1,2, riri, KiKi, αiαi, τiτi, σiσi (i=1,2i=1,2) are functions of period ω>0ω>0.