Analysis And Synchronization Of Chaotic Finance System With Non-constant Demand Elasticity

Finance system is a complex nonlinear system.When it is disturbed by ex-ternal factors,the inherent instability of the system itself may lead to chaos and exhibit unpredictable economic behavior.Therefore,the theoretical research on the stability and control of chaotic finance system is very importantThe problems on the dynamics and synchronization of chaotic finance system with non-constant demand elasticity are studied in this paper.Firstly,the stabili-ty of all equilibrium points of the system is discussed by using Hartman-Grobman theorem,and the conditions of asymptotic stability of equilibrium points are given Secondly,the existence of the Hopf bifurcation of the system at one of the equilib-rium points is verified by using the Hopf bifurcation theorem.The direction and stability of the Hopf bifurcation of the system at the equilibrium point are given by combining the center manifold theory and the normal form theory,and the numer-ical simulation is carried out.Finally,in the case of uncertain parameters,for the drive response system composed of two chaotic finance systems with non-constant demand elasticity,the adaptive control law and parameter estimation updated law are proposed by using Lyapunov stability theory.It is proved that the drive response system achieves function Q-S synchronization and generalized function projection synchronization.The effectiveness of the proposed adaptive control law is verified by numerical simulation.