Abstract:
The existence of positive solutions of the steady-state system are discussed for cooperative model with saturating terms for two species under the first boundary conditions. First, the prior estimate of the solutions is given by the monotone method; by means of local bifurcation theory, the system bifurcations at two semi-trivial solutions for two cases(λ１－ｃ＜ａ＜λ１ and ａ＞λ１) are studied, respectively. It is proved that positive solutions exist in some neighborhoods of (β，０，θβ) and (ｂ′，θａ，０), respectively. Finally, the global bifurcations are investigated by the global bifurcation theory, and the existence of positive solutions of the steady-state system for the two cases are obtained accordingly.
