一类综合国力模型的全局分歧

摘要

研究了一类具有扩散的综合国力模型,以扩散系数d为分歧参数,运用分歧理论和度理论的知识,讨论了在一定条件下系统在正常数平衡态解附近的分歧现象,证明了在点（dj,U＊）处可产生局部分歧jΓ,并给出了分歧点附近解的结构,同时利用全局分歧理论得出局部分歧jΓ可以延拓为全局分歧Γ.%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.