金融市场中递增扩张映射模型的混沌吸引子分叉

Chaotic attractor bifurcation of incremental expansion map model in financial market

对TRAMONTANAF等人的模型进行了简化,提出了有两个不连续点的一维映射模型,重点研究描述了该模型的递增扩张映射的混沌吸引子的相关分叉:首先研究排斥环的同宿分叉,并在参数平面(m_(L),m_(R))上确定混沌存在的区域,然后给出混沌吸引子边界碰撞分叉,并解释了引起吸引子几何结构变化的机理.

In this paper,the model of TRAMONTANA F,et al is simplified,and a 1-dimensional map model with two discontinuous points is proposed,which focus on the correlation bifurcation of the chaotic attractor of the incremental expansion map in the model.Firstly,the homoclinic bifurcation of repulsive cycle is studied,and the existence region of chaos is determined on the parameter plane(m_(L),m_(R)).Then the boundary collision bifurcation of chaotic attractor is given,and the mechanism of the change of attractor geometry structure is explained.