基于利率浮动阈值条件下一类分数阶金融系统动力学特征及其仿真研究

Simulated Dynamics Complexity of Fractional Financial System with Floating Rates of Interest

利用混沌与分岔理论研究了一类基于利率浮动阈值条件的分数阶金融系统动力学行为。首先,分析了系统的稳定性,平衡点.其次,借助预估校正法,数值仿真了关于微分阶数,储蓄量,投资成本和商品需求弹性的分岔图、相图,结合分岔图、相图、Lyapunov指数分析了该系统具有的复杂动力学行为,研究了各金融指标对系统复杂演化行为的影响,并给出了相应的Lyapunov指数的演化特性图,所得结果为金融管理部门进行宏观调控提供了理论支持。

In this paper,the chaos and bifurcation theory are used to study the dynamic behavior of a class of fractional financial system with floating rates of interest.Firstly,the stability of the system and the equilibrium point are analyzed.Secondly,with the predictorcorrector method,the bifurcation diagram and phase diagram about the differential order,savings,investment cost and commodity demand elasticity are numerically simulated.From the bifurcation diagram and phase diagram,the evolution characteristics of Lyapunov index it can be obtained that the system has complex dynamic behavior.Combined with the analysis of various financial indicators,the research results provide a theoretical basis for the financial regulation system of relevant departments.