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

Authors:
Yonghui Xia;Jinde Cao
Affiliations:
College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, P.R. China;Department of Mathematics, Southeast University, Nanjing 210096, P.R. China
Venue:
Computers & Mathematics with Applications
Year:
2006

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Abstract

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)=x"i(t)b"i(t)-@?k=1na"i"k(t)x"k(t-T"i"k)-@?l=1mc"i"l(t)yl(t-@s"i"l),i=1,2,...,n,y@?"j(t)=y"j(t)-r"j(t)+@?k=1nd"j"k(t)x"k(t-@x"j"k)-@?l=1me"j"l(t)yl(t-@h"j"l),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.