Chaotic Characteristics Analysis And Control Of A Class Of Financial Systems

With the development of economic globalization,financial order has become more complex,changeable and difficult to predict.Then there are many urgent problems to be solved,such as chaos,multi-stability and control of the financial systems,which have attracted more and more attention.This paper studies chaotic characteristics and control of a class of financial systems.The main innovative work is as follows:(1)This paper studies a class of financial systems with chaotic characteristics: a hyperchaotic financial system,a chaotic financial system with nonconstant demand elasticity and a chaotic financial system with average profit margin.Through the analysis of equilibrium points and stability,both multi-stability and Hopf bifurcation are found to exist in this class of financial systems.At the same time,multi-stability and Hopf bifurcation phenomena are also numerically given,which shows complex dynamics of this class of financial systems from the viewpoint of numerical analysis.In addition,abundant transient phenomena are found in a hyperchaotic financial system,and the path from period-doubling bifurcation to chaos is found in a chaotic financial system with nonconstant demand elasticity.All these further illustrate complex dynamics of this class of financial systems.(2)According to complex dynamics of this class of financial systems,displacement feedback controller and speed feedback controller are designed to control a hyperchaotic financial system,a chaotic financial system with nonconstant demand elasticity and a chaotic financial system with average profit margin respectively.The value range of controller parameters is obtained theoretically,by adjusting the displacement feedback coefficient and the velocity feedback coefficient,all the systems are controlled from chaotic state to stable state.Results from the numerical analysis show that the two control methods have good applicability to this class of financial systems,and can achieve excellent control effect.(3)Based on this class of financial systems,a new improved hyperchaotic system with two positive Lyapunov exponents is found.By transforming the improved hyperchaotic system into Kolmogorov type system,the reason why chaos exist in the system is studied from the perspective of energy,and the external energy is found to be the main factor that it can generate chaos.At the same time,by combining the improved hyperchaotic system with practice,explains dynamic behaviors of the improved hyperchaotic system,and shows that the improved hyperchaotic system can more accurately describe dynamics of financial market.In addition,from the perspective of Hamiltonian energy,a Hamiltonian energy feedback controller is designed to control it.At the same time,the displacement feedback controler and the velocity feedback controler are also designed to control it.All three methods can control the improved hyperchaotic system from chaotic state to stable state.