一类分数阶非线性金融系统的复杂度仿真研究  

Complexity Simulation of a Class of Fractional-order Nonlinear Financial System

作　　者：高忠社[1] GAO Zhongshe(School of Mathematics and Statistics,Tianshui Normal University,Gansu Tianshui 741001,China)

机构地区：[1]天水师范学院数学与统计学院,甘肃天水741001

出　　处：《河北师范大学学报（自然科学版）》2022年第2期147-153,共7页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(11561060);甘肃省数学省级重点学科建设项目(甘学位[2018]15号);甘肃省高等学校创新能力提升项目(2021B-221);天水师范学院创新基金(CXJ2020-11);天水师范学院伏羲创新团队建设项目(FXD2020-03)。

摘　　要：利用混沌与分岔理论研究了一类分数阶金融系统的混沌动力学行为.首先,分析了该系统的稳定性、平衡点.其次,借助预估校正法,得到了关于微分阶数储蓄量、投资成本和商品需求弹性的分岔图、相图和时间历程图,由分岔图和相图可知该系统会出现非常复杂的动力学行为,利用混沌与分岔理论进一步研究了不同参数配比的相关问题,分别模拟了各金融指标对分数阶金融系统复杂性演化行为的影响,得出了一些有意义的结果,可以为经济金融管理部门对金融系统调控提供理论依据.The chaos dynamic behaviors of a class of fractional order financial systems based on chaos and bifurcation theory were discussed in this paper.Firstly,the stability of the system and the equilibrium point are analyzed.Secondly,the bifurcation diagram and phase diagram of differential order,savings,investment cost and commodity demand elasticity are obtained by a predictive correction method.The bifurcation diagram and phase diagram show that the system will have very complex dynamic behaviors.Furthermore,how to use the chaos theory of mixed bifurcation under different parameter ratios was studied,simulates the influence of various financial indicators on the complexity evolution behavior of fractional financial system was simulated,and obtains some meaningful re-search results was obtained.These results provides a theoretical basis for the financial managers to regulate the financial system.

关 键 词：分数阶理论 金融系统 分岔理论 吸引子 

分 类 号：O322[理学—一般力学与力学基础]