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

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 law...

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Vydané v:Advances in difference equations Ročník 2019; číslo 1; s. 1 - 23
Hlavní autori: Khennaoui, Amina-Aicha, Ouannas, Adel, Bendoukha, Samir, Grassi, Giuseppe, Wang, Xiong, Pham, Viet-Thanh, Alsaadi, Fawaz E.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 26.09.2019
Springer Nature B.V
SpringerOpen
Predmet:
Advances in Fractional Differential Equations and Their Real World Applications - Part Two
Analysis
Bifurcations
Chaos theory
Control
Control stability
Control theory
Difference and Functional Equations
Difference equations
Discrete systems
Fractional discrete-time calculus
Fractional Rössler map
Fractional Stefanski map
Fractional Wang map
Functional Analysis
Liapunov exponents
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Synchronism
Synchronization
34H10
Fractional Wang map
Control
Fractional discrete-time calculus
Fractional Stefanski map
Synchronization
Fractional Rössler map
34D06
34A08
ISSN:1687-1847, 1687-1839, 1687-1847
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Popis
Shrnutí: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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-019-2343-6