Chaos, control, and synchronization in some fractional-order difference equations

Advances in Difference Equations

Fawaz E. Alsaadi¹  Adel Ouannas²  Giuseppe Grassi³  Samir Bendoukha⁴  Xiong Wang⁵  Amina-Aicha Khennaoui⁶  Viet-Thanh Pham⁷ 

[1] Department of Information Technology, Faculty of Computing and IT, King Abdulaziz University;Department of Mathematics and Computer Science, University of Larbi Tebessi;Dipartimento Ingegneria Innovazione, Universita del Salento;Electrical Engineering Department, College of Engineering at Yanbu, Taibah University;Institute for Advanced Study, Shenzhen University;Laboratory of Dynamical System and Control, University of Larbi Ben M’hidi;Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University;

关键词: Fractional discrete-time calculus;    Fractional Stefanski map;    Fractional Rössler map;    Fractional Wang map;    Control;    Synchronization;   

DOI  :  10.1186/s13662-019-2343-6

来源: DOAJ

【 摘 要 】

Abstract In this paper, we propose three fractional chaotic maps based on the well known 3D Stefanski, Rössler, and Wang maps. The dynamics of the proposed fractional maps are investigated experimentally by means of phase portraits, bifurcation diagrams, and Lyapunov exponents. In addition, three control laws are introduced for these fractional maps and the convergence of the controlled states towards zero is guaranteed by means of the stability theory of linear fractional discrete systems. Furthermore, a combined synchronization scheme is introduced whereby the fractional Rössler map is considered as a drive system with the response system being a combination of the remaining two maps. Numerical results are presented throughout the paper to illustrate the findings.

【 授权许可】

Unknown