Application of Mawhin's Coincidence Degree and Matrix Spectral Theory to a Delayed System

Abstract

This paper gives an application of Mawhin’s coincidence degree and matrix spectral theory to a predator-prey model withM-predators andN-preys. The method is different from that used in the previous work. Some new sufficient conditions are obtained for the existence and global asymptotic stability of the periodic solution. The existence and stability conditions are given in terms of spectral radius of explicit matrices which are much different from the conditions given by the algebraic inequalities. Finally, an example is given to show the feasibility of our results.