Global attractivity of a periodic ecological model with m-predators and n-preys by “Pure-delay type” system

In this paper, based on the comparison theorem and Lyapunov method, we study the following periodic Lotka-Volterra model with m-predators and n-preys by “pure-delay type”:x˙i(t)=xi(t)bi(t)−∑k=1naik(t)xk(t−Tik)−∑l=1mcil(t)yl(t−σil), i=1,2,…,n,y˙j(t)=yj(t)−rj(t)+∑k=1ndjk(t)xk(t−ξjk)−∑l=1mejl(t)yl(t−ηjl), j=1,2,…,m.By proposing a new concept of generalized uniform M-matrix, a set of easily verifiable sufficient conditions are obtained for the existence and global attractivity of a unique positive periodic solution of the above model. The obtained results improve and generalize some known results.