Periodic bifurcation solution for a delay competition diffusion system

This paper investigates the Hopf bifurcation of a delay competition diffusi on system. Our purpose is to give more detail information about the Hopf bi furcation solutions of this system. We derive the basis of the eigenfunctio n subspace then convert the existence of the periodic bifurcation solution to the study of the existence of the implicit function and obtain the asymp totic expression of periodic solutions. Moreover we determine the bifurcati on direction which is useful for analyzing the properties of periodic solut ions.