Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System

This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under effective impulse macroeconomic management means. Matlab's LMI toolbox is utilized to deduce the feasible solution in a numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.

Automated summary

This paper presents a new global Mittag-Leffler synchronization criterion for fractional-order hyper-chaotic financial systems by designing impulsive control and state feedback controller. The significance lies in achieving synchronization between backward and advanced economic systems under effective impulse macroeconomic management means. The effectiveness of the proposed methods is demonstrated in a numerical example, overcoming the mathematical difficulty of non-Lipschitz continuous activation function.