Chaos control strategy for a fractional-order financial model

Advances in Difference Equations

Changjin Xu¹  Maoxin Liao²  Zixin Liu³  Peiluan Li⁴  Chaouki Aouiti⁵ 

[1]Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, 550004, Guiyang, P.R. China

[2]School of Mathematics and Physics, University of South China, 421001, Hengyang, P.R. China

[3]School of Mathematics and Statistics, Guizhou University of Finance and Economics, 550004, Guiyang, P.R. China

[4]School of Mathematics and Statistics, Henan University of Science and Technology, 471023, Luoyang, P.R. China

[5]UR13ES47 Research Units of Mathematics and Applications, Faculté des Sciences de Bizerte, Université de Carthage, 7021, Bizerte, Tunisie

关键词: Chaos control;    Financial model;    Stability;    Hopf bifurcation;    Fractional order;    Delay;    34C23;    34K18;    37K15;    39A11;    92B20;   

DOI  :  10.1186/s13662-020-02999-x

来源: Springer

【 摘 要 】

In this paper, we propose a new fractional-order financial model which is a generalized version of the financial model reported in the previous publications. By applying a suitable time-delayed feedback controller, we have control for the chaotic behavior of the fractional-order financial model. We investigate the stability and the existence of a Hopf bifurcation of the fractional-order financial model. A new sufficient condition that guarantees the stability and the existence of a Hopf bifurcation for a fractional-order delayed financial model is presented by regarding the delay as bifurcation parameter. The investigation shows that the delay and the fractional order have an important effect on the stability and Hopf bifurcation of involved model. Some simulations justifying the validity of the derived analytical results are given. The obtained results of this article are innovative and are of great significance in handling the financial issues.

【 授权许可】

CC BY