Study on Chaos Created by Hopf Bifurcation of One Kind of Financial System and Its Application

From a mathematical model of one kind complicated financial system, corresponding local topological structures of such kind system on condition of certain parametercombination, unstable equilibrium point of the system, conditions on which Hopf bifurcation is created and stability of the limit circle corresponding to the Hopf bifurcation as well as condition on which the limit circle is stable have been studied. From relationship between each parameter and the Hopf bifurcation all the way to route which leads to chaos etc have been studied. Following the above, conditions on which complicated behaviors created locally in such kind system has been analyzed. By applying fractal dimension, Lyapunov index, the intrinsic complexity of the system on such condition has been studied, and result of the numerical simulation proves the theory of this paper correct.