Existence and global attractivity of a periodic solution for a prey-predator model with sex-structure

In this paper, we investigate the following periodic sex-structure model:x1′(t)=x1(t)b1(t)x2(t)x1(t)-d1(t)-k(t)x1(t)-k(t)x2(t)-c1(t)x3(t),x2′(t)=x2(t)β(t)-k(t)x1(t)-k(t)x2(t)-c1(t)x3(t),x3′(t)=x3(t)-a(t)-b(t)x3(t)+c2(t)x1(t)+c2(t)x2(t).The sufficient and realistic conditions are obtained for the existence of positive periodic solution of above system. Further, by constructing a V functional and using the result of the existence of positive periodic solutions, the global attractivity of a positive periodic solution for above system is obtained.