Four - Synchronization between fractional chaotic maps with different dimensions

Adel Ouannas; Amina Aicha Khennaoui; Iqbal M. Batiha; Viet Thanh Pham

doi:10.1016/B978-0-32-390090-4.00009-3

Four - Synchronization between fractional chaotic maps with different dimensions

Adel Ouannas
, Amina Aicha Khennaoui
, Iqbal M. Batiha
, Viet Thanh Pham

University of Oum El Bouaghi
University of Jordan
Ton Duc Thang University

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

11 Scopus citations

Abstract

Recently, numerous chaotic systems in the form of fractional difference equations have received considerable attention. Based on the stability theory of linear fractional difference systems, this chapter presents combined synchronization between fractional-order chaotic maps described by the left Caputo difference operator. Some nonlinear controllers are designed, which enable synchronization to be achieved between different fractional-order chaotic maps with different dimensions. The 2D fractional Lozi, Lorenz, and Flow maps, as well as the 3D fractional Wang, Rössler, and Stefanski maps, have been taken to show the combined synchronization. The results of these synchronization laws are experimentally investigated to ensure that the synchronization errors converge to zero.

Original language	English
Title of host publication	Fractional-Order Design
Subtitle of host publication	Devices, Circuits, and Systems
Publisher	Elsevier
Pages	89-121
Number of pages	33
ISBN (Electronic)	9780323900904
ISBN (Print)	9780323902045
DOIs	https://doi.org/10.1016/B978-0-32-390090-4.00009-3
State	Published - 1 Jan 2021
Externally published	Yes

Keywords

Chaotic maps
Combined synchronization
Discrete fractional calculus
Linearization method
Three-dimensional system
Two-dimensional system

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10.1016/B978-0-32-390090-4.00009-3

Cite this

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title = "Four - Synchronization between fractional chaotic maps with different dimensions",

abstract = "Recently, numerous chaotic systems in the form of fractional difference equations have received considerable attention. Based on the stability theory of linear fractional difference systems, this chapter presents combined synchronization between fractional-order chaotic maps described by the left Caputo difference operator. Some nonlinear controllers are designed, which enable synchronization to be achieved between different fractional-order chaotic maps with different dimensions. The 2D fractional Lozi, Lorenz, and Flow maps, as well as the 3D fractional Wang, R{\"o}ssler, and Stefanski maps, have been taken to show the combined synchronization. The results of these synchronization laws are experimentally investigated to ensure that the synchronization errors converge to zero.",

keywords = "Chaotic maps, Combined synchronization, Discrete fractional calculus, Linearization method, Three-dimensional system, Two-dimensional system",

author = "Adel Ouannas and Khennaoui, \{Amina Aicha\} and Batiha, \{Iqbal M.\} and Pham, \{Viet Thanh\}",

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doi = "10.1016/B978-0-32-390090-4.00009-3",

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T1 - Four - Synchronization between fractional chaotic maps with different dimensions

AU - Ouannas, Adel

AU - Khennaoui, Amina Aicha

AU - Batiha, Iqbal M.

AU - Pham, Viet Thanh

PY - 2021/1/1

Y1 - 2021/1/1

N2 - Recently, numerous chaotic systems in the form of fractional difference equations have received considerable attention. Based on the stability theory of linear fractional difference systems, this chapter presents combined synchronization between fractional-order chaotic maps described by the left Caputo difference operator. Some nonlinear controllers are designed, which enable synchronization to be achieved between different fractional-order chaotic maps with different dimensions. The 2D fractional Lozi, Lorenz, and Flow maps, as well as the 3D fractional Wang, Rössler, and Stefanski maps, have been taken to show the combined synchronization. The results of these synchronization laws are experimentally investigated to ensure that the synchronization errors converge to zero.

AB - Recently, numerous chaotic systems in the form of fractional difference equations have received considerable attention. Based on the stability theory of linear fractional difference systems, this chapter presents combined synchronization between fractional-order chaotic maps described by the left Caputo difference operator. Some nonlinear controllers are designed, which enable synchronization to be achieved between different fractional-order chaotic maps with different dimensions. The 2D fractional Lozi, Lorenz, and Flow maps, as well as the 3D fractional Wang, Rössler, and Stefanski maps, have been taken to show the combined synchronization. The results of these synchronization laws are experimentally investigated to ensure that the synchronization errors converge to zero.

KW - Chaotic maps

KW - Combined synchronization

KW - Discrete fractional calculus

KW - Linearization method

KW - Three-dimensional system

KW - Two-dimensional system

UR - https://www.scopus.com/pages/publications/85129830743

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DO - 10.1016/B978-0-32-390090-4.00009-3

M3 - Chapter

AN - SCOPUS:85129830743

SN - 9780323902045

SP - 89

EP - 121

BT - Fractional-Order Design

PB - Elsevier

ER -

Four - Synchronization between fractional chaotic maps with different dimensions

Abstract

Keywords

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