Dynamics and function projection synchronization for the fractional-order financial risk system

The real financial market has long-term memory and complexity characteristics. To describe a more realistic financial risk management process , this paper introduces Caputo fractional derivative to construct a fractional-order financial risk system (FFRS). Adomian decomposition method is applied to get numerical solutions of the FFRS. The effects of order and parameters on system dynamics are investigated through bifurcation diagrams , Lyapunov exponents spectrum and spectral entropy complexity. The results show the range of chaotic state is smaller or the largest Lyapunov exponent is reduced at suitable order and parameters. The dynamic results are explained by real financial risk management process. In addition, state transition phenomenon of the FFRS is discussed. To control and predict the system in chaotic state, the function projection synchronization is applied. Dynamics and synchronization of the system have reference significance for financial risk management.