Bifurcation And Synchronization Of A Hyperchaotic Financial System

As a complex nonlinear system,the financial system will produce chaos when it is disturbed by the outside world,which will lead to unpredictable economic fluctuations,therefore,it is of great value to analyze the bifurcation and chaos synchronization of financial system.In this paper,we mainly study bifurcation and synchronization of a hyperchaot-ic financial system.On one hand,the existence of the Hopf bifurcation at equilibri-um point of the system is discussed by the center manifold and normal form theories,further we prove the bifurcation direction and stability of generating periodic so-lutions.On the other hand,based on the stability theory of Lyapunov,adaptive control law and parameter updated law are proposed for the driver-response system,to realize the generalized function projective synchronization of the driver-response system.Numerical simulation verifies the effectiveness of synchronization.