基于非退化平衡点的分数阶混沌经济系统演化规律研究

摘要

基于非线性复杂经济系统中的部分变量具有长期的记忆性,利用整数阶微积分理论不能描述其演化特征,而利用分数阶微积分理论可以对其进行建模演化分析.在定性分析一类分数阶混沌经济系统平衡点的稳定性基础上,研究了该系统非退化平衡点附近的复杂性演化规律以及在此平衡点渐近混沌状态的发生条件,利用Block-by-Block算法对该混沌经济系统非退化平衡点的演化进行时间序列图与相图仿真研究.结果表明,基于投资需求和微分阶数的变化,该经济系统演化处于不同的稳定状态,为政府调控经济系统提供理论依据.%Due to some variables had long-term memory in the nonlinear complex economic system,with the characteristics of integer order calculus theory couldn't describe,it can use the fractional calculus theory to analyze the evolution of the model.This paper qualitatively analyzed a class of fractional order chaotic economic system based on the stability of equilibrium point,and studied the complexity evolution law of the system and the occurrence condition of the asymptotic chaotic state in the nondegenerate equilibrium point.It used Block-by-Block algorithm to study the evolution of the non-degenerate equilibrium point of the chaotic economic system and the simulation of the time series diagram and phase diagram.The results show that the evolution of the economic system is in a different stable state based on the change of the investment demand and the differential order and it provides a theoretical basis for the government to control the economic system.