Chaos in fractional-order difference systems

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

doi:10.1016/B978-0-12-824293-3.00011-9

Chaos in fractional-order difference systems

Amina Aicha Khennaoui
, Adel Ouannas
, 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

2 Scopus citations

Abstract

The study of the chaotic dynamics in fractional-order maps has received great attention in the past years. This chapter proposes 2D and 3D fractional maps based on the Caputo difference operator. The dynamics of these fractional systems are experimentally investigated via bifurcation diagrams, phase portraits, the maximum Lyapunov exponent, and the 0-1 test. Results show that the 2D fractional map shows coexistence of different types of periodic attractors and chaotic attractors. Additionally, the dynamics and complexity of the 3D fractional map shows high complexity as the fractional order decreases.

Original language	English
Title of host publication	Fractional Order Systems
Subtitle of host publication	An Overview of Mathematics, Design, and Applications for Engineers
Publisher	Elsevier
Pages	257-286
Number of pages	30
ISBN (Electronic)	9780128242933
ISBN (Print)	9780128243343
DOIs	https://doi.org/10.1016/B978-0-12-824293-3.00011-9
State	Published - 1 Jan 2021
Externally published	Yes

Keywords

Bifurcation diagrams
Chaotic maps
Discrete fractional calculus
Lyapunov exponents

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10.1016/B978-0-12-824293-3.00011-9

Cite this

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title = "Chaos in fractional-order difference systems",

abstract = "The study of the chaotic dynamics in fractional-order maps has received great attention in the past years. This chapter proposes 2D and 3D fractional maps based on the Caputo difference operator. The dynamics of these fractional systems are experimentally investigated via bifurcation diagrams, phase portraits, the maximum Lyapunov exponent, and the 0-1 test. Results show that the 2D fractional map shows coexistence of different types of periodic attractors and chaotic attractors. Additionally, the dynamics and complexity of the 3D fractional map shows high complexity as the fractional order decreases.",

keywords = "Bifurcation diagrams, Chaotic maps, Discrete fractional calculus, Lyapunov exponents",

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

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T1 - Chaos in fractional-order difference systems

AU - Khennaoui, Amina Aicha

AU - Ouannas, Adel

AU - Batiha, Iqbal M.

AU - Pham, Viet Thanh

PY - 2021/1/1

Y1 - 2021/1/1

N2 - The study of the chaotic dynamics in fractional-order maps has received great attention in the past years. This chapter proposes 2D and 3D fractional maps based on the Caputo difference operator. The dynamics of these fractional systems are experimentally investigated via bifurcation diagrams, phase portraits, the maximum Lyapunov exponent, and the 0-1 test. Results show that the 2D fractional map shows coexistence of different types of periodic attractors and chaotic attractors. Additionally, the dynamics and complexity of the 3D fractional map shows high complexity as the fractional order decreases.

AB - The study of the chaotic dynamics in fractional-order maps has received great attention in the past years. This chapter proposes 2D and 3D fractional maps based on the Caputo difference operator. The dynamics of these fractional systems are experimentally investigated via bifurcation diagrams, phase portraits, the maximum Lyapunov exponent, and the 0-1 test. Results show that the 2D fractional map shows coexistence of different types of periodic attractors and chaotic attractors. Additionally, the dynamics and complexity of the 3D fractional map shows high complexity as the fractional order decreases.

KW - Bifurcation diagrams

KW - Chaotic maps

KW - Discrete fractional calculus

KW - Lyapunov exponents

UR - https://www.scopus.com/pages/publications/85129415113

U2 - 10.1016/B978-0-12-824293-3.00011-9

DO - 10.1016/B978-0-12-824293-3.00011-9

M3 - Chapter

AN - SCOPUS:85129415113

SN - 9780128243343

SP - 257

EP - 286

BT - Fractional Order Systems

PB - Elsevier

ER -

Chaos in fractional-order difference systems

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Keywords

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