一维资产价格模型BCB曲线和周期结构  

BCB curves and periodic structure of one-dimensional asset price model

作　　者：顾恩国[1] 倪俊 何昭辉 GU Enguo;NI Jun;HE Zhaohui(College of Mathematics and Statistics,South-Central Minzu University,Wuhan 430074,China)

机构地区：[1]中南民族大学数学与统计学学院,武汉430074

出　　处：《中南民族大学学报（自然科学版）》2023年第1期134-140,共7页Journal of South-Central University for Nationalities：Natural Science Edition

基　　金：国家自然科学基金资助项目(61703442);中央高校基本科研业务费专项资金资助项目(CZT20006)。

摘　　要：研究了具有两个不连续点的一维分段线性映射的边界碰撞分叉,该模型反映了金融市场的资产价格围绕基本价值波动的规律,其特征是3个线性子系统具有相同的斜率.假设模型的斜率都在-1和1之间,运用Leonov方法计算分叉曲线,进而讨论参数平面(s,m)中的周期结构,发现多个不连续点映射的周期叠加结构的新情况,利用首次返回映射证明了多吸引子共存的问题.The border collision bifurcations occurring in a one-dimensional piecewise liner map with two discontinuity points is investigated.The model reflects the law of asset price fluctuation around basic value in financial market,characterized by the same slope rate of three linear subsystems.It is assumed that the slopes of the models are between-1 and 1,bifurcation curves by Leonov method is calculated,and periodic structure in parametric plane(s,m)is discussed to find a new case of period adding structure of multiple discontinuous point maps and the coexistence of multiple attractors is proved by the first return map.

关 键 词：边界碰撞分叉 周期结构 第一复杂度 多吸引子共存 首次返回映射 

分 类 号：O192[理学—数学]