Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Xinggui Li
,
Ruofeng Rao
* ,
Shouming Zhong
,
Xinsong Yang
,
Hu Li
,
Yulin Zhang
Version 1 : Received: 6 July 2022 / Approved: 7 July 2022 / Online: 7 July 2022 (09:04:05 CEST)
Version 2 : Received: 7 July 2022 / Approved: 8 July 2022 / Online: 8 July 2022 (10:31:03 CEST)

A peer-reviewed article of this Preprint also exists.

Li, X.; Rao, R.; Zhong, S.; Yang, X.; Li, H.; Zhang, Y. Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System. Mathematics 2022, 10, 2737. Li, X.; Rao, R.; Zhong, S.; Yang, X.; Li, H.; Zhang, Y. Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System. Mathematics 2022, 10, 2737.

Abstract

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 the effective impulse macroeconomic management means. Matlab LMI-toolbox is utilized to deduce the feasible solution in 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.

Keywords

Mittag-Leffler stability; Caputo fractional-order derivative; non-Lipschitz continuity; hyper-chaotic financial system; Mittag-Leffler function

Subject

Computer Science and Mathematics, Applied Mathematics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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