Hopf Bifurcation Of Traveling Wave Solution Of Two Partial Functional Differential Equations

This paper mainly discussed that delay term had impact on traveling wave solution of two partial functional differential equations employing the method of stability of equilibrium and theory of Hopf bifurcation. In 2001 years, Wu Jianhong[1] acquired the existence about the traveling wave solution of delay Fish-Kpp equation and in 2001years, Joseph W.-H. So, Xingfu Zou[2] also acquired the existence about the traveling wave solution of delay Nicholson's Blowfies equationWhen the above two equations have traveling wave solution u ( x ,t )= ? ( z),z = x + ctand N ( x ,t )= ? ( z), z = x + ct, we can transform the above equations into delay differential equations respectively as follows:We employed method of equilibrium stability and theory of Hopf bifurcation to research the qualitative behavior of the traveling wave solution of the partial functional differential equations and found that delay term has important impact on the traveling wave solution and when delay term across a certain delay valueτ0it will become periodic traveling solution.