Global bifurcation of a class of synthetical national power model

A class of synthetical national power models with diffusion is investigated.Using diffusion coefficient as the bifurcation parameter,the bifurcation at positive constant steady-state solution is obtained by the bifurcation theory and degree theory.The local bifurcation at the point(dj,U*) is proved,and the structure of solution near the bifurcation point is given.At the same time,by means of the global bifurcation theorem,it is shown that the local bifurcation can be extended to global bifurcation.