一类经济大系统模型的建立及其Hopf分支

Modeling a Large-Scale Economic System and Hopf Bifurcation

摘要: 本文首先以非线性时滞大系统为理论基础建立了一类经济大系统模型，该模型以商品价格为关键因素。接着以τ为参考元素研究了该模型的稳定性及Hopf分叉，发现当τ变化时，该系统的稳定性会发生变化，该模型会在某一确定值处出现Hopf分叉。最后用中心流形定理和规范形方法给出了分拆周期解的若干稳定性结果。

Abstract: Taking the time delay non-linear large-scale system as the theoretical basis, the large-scale eco-nomic system is modeled, which takes the price of commodity as the key elements. Then, the sta-bility and Hopf bifurcation of the system model are studied by introducing a delay as a parameter. It is found that the Hopf bifurcation occurs when τ crosses some critical values. By using the center manifold method and normal form theory, some stability results are given for the periodic solution of the system.