Hardware Implementation of a Two-dimensional Fractional Map with Hidden Attractors

Adel Ouannas; Amina Aicha Khennaoui; Giuseppe Grassi; Viet Thanh Pham; Zohir Dibi; Shaher Momani

doi:10.1109/ICFDA58234.2023.10153323

Hardware Implementation of a Two-dimensional Fractional Map with Hidden Attractors

Adel Ouannas
, Amina Aicha Khennaoui
, Giuseppe Grassi
, Viet Thanh Pham
, Zohir Dibi
, Shaher Momani

Nonlinear Dynamic Research Centre (NDRC)

University of Oum El Bouaghi
Abdelhamid Mehri Constantine 2 University
University of Salento
Ton Duc Thang University

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

6 Scopus citations

Abstract

Several efforts have been recently devoted to the hardware implementations of fractional systems. This manuscript makes a contribution to the topic by introducing the first example of hardware implementation of a 2D fractional map with hidden. Specifically, the paper presents first a new class of two-dimensional fractional map with no equilibruim points using the Grunwald-Letnikov difference operator. Then, the system dynamics are analyzed via numerical simulation, such as bifurcation diagrams, Lyapunov exponents and phase portraits. Finally, the paper illustrates a hardware implementation of the 2D fractional map via a microcontroller, with the aim to show the real presence of chaotic hidden attractors in physical systems described by non-integer order maps.

Original language	English
Title of host publication	2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9798350321685
DOIs	https://doi.org/10.1109/ICFDA58234.2023.10153323
State	Published - 2023
Event	2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023 - Ajman, United Arab Emirates Duration: 14 Mar 2023 → 16 Mar 2023

Publication series

Name	2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

Conference

Conference	2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023
Country/Territory	United Arab Emirates
City	Ajman
Period	14/03/23 → 16/03/23

Keywords

Discrete fractional calculus
Hardware implementation
chaotic map

Access to Document

10.1109/ICFDA58234.2023.10153323

Cite this

Ouannas, A., Khennaoui, A. A., Grassi, G., Pham, V. T., Dibi, Z., & Momani, S. (2023). Hardware Implementation of a Two-dimensional Fractional Map with Hidden Attractors. In 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023 (2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICFDA58234.2023.10153323

Ouannas, Adel ; Khennaoui, Amina Aicha ; Grassi, Giuseppe et al. / Hardware Implementation of a Two-dimensional Fractional Map with Hidden Attractors. 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023. Institute of Electrical and Electronics Engineers Inc., 2023. (2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023).

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title = "Hardware Implementation of a Two-dimensional Fractional Map with Hidden Attractors",

abstract = "Several efforts have been recently devoted to the hardware implementations of fractional systems. This manuscript makes a contribution to the topic by introducing the first example of hardware implementation of a 2D fractional map with hidden. Specifically, the paper presents first a new class of two-dimensional fractional map with no equilibruim points using the Grunwald-Letnikov difference operator. Then, the system dynamics are analyzed via numerical simulation, such as bifurcation diagrams, Lyapunov exponents and phase portraits. Finally, the paper illustrates a hardware implementation of the 2D fractional map via a microcontroller, with the aim to show the real presence of chaotic hidden attractors in physical systems described by non-integer order maps.",

keywords = "Discrete fractional calculus, Hardware implementation, chaotic map",

author = "Adel Ouannas and Khennaoui, \{Amina Aicha\} and Giuseppe Grassi and Pham, \{Viet Thanh\} and Zohir Dibi and Shaher Momani",

note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023 ; Conference date: 14-03-2023 Through 16-03-2023",

year = "2023",

doi = "10.1109/ICFDA58234.2023.10153323",

language = "English",

series = "2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

booktitle = "2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023",

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}

Ouannas, A, Khennaoui, AA, Grassi, G, Pham, VT, Dibi, Z & Momani, S 2023, Hardware Implementation of a Two-dimensional Fractional Map with Hidden Attractors. in 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023. 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023, Institute of Electrical and Electronics Engineers Inc., 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023, Ajman, United Arab Emirates, 14/03/23. https://doi.org/10.1109/ICFDA58234.2023.10153323

Hardware Implementation of a Two-dimensional Fractional Map with Hidden Attractors. / Ouannas, Adel; Khennaoui, Amina Aicha; Grassi, Giuseppe et al.
2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023. Institute of Electrical and Electronics Engineers Inc., 2023. (2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023).

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

TY - GEN

T1 - Hardware Implementation of a Two-dimensional Fractional Map with Hidden Attractors

AU - Ouannas, Adel

AU - Khennaoui, Amina Aicha

AU - Grassi, Giuseppe

AU - Pham, Viet Thanh

AU - Dibi, Zohir

AU - Momani, Shaher

PY - 2023

Y1 - 2023

N2 - Several efforts have been recently devoted to the hardware implementations of fractional systems. This manuscript makes a contribution to the topic by introducing the first example of hardware implementation of a 2D fractional map with hidden. Specifically, the paper presents first a new class of two-dimensional fractional map with no equilibruim points using the Grunwald-Letnikov difference operator. Then, the system dynamics are analyzed via numerical simulation, such as bifurcation diagrams, Lyapunov exponents and phase portraits. Finally, the paper illustrates a hardware implementation of the 2D fractional map via a microcontroller, with the aim to show the real presence of chaotic hidden attractors in physical systems described by non-integer order maps.

AB - Several efforts have been recently devoted to the hardware implementations of fractional systems. This manuscript makes a contribution to the topic by introducing the first example of hardware implementation of a 2D fractional map with hidden. Specifically, the paper presents first a new class of two-dimensional fractional map with no equilibruim points using the Grunwald-Letnikov difference operator. Then, the system dynamics are analyzed via numerical simulation, such as bifurcation diagrams, Lyapunov exponents and phase portraits. Finally, the paper illustrates a hardware implementation of the 2D fractional map via a microcontroller, with the aim to show the real presence of chaotic hidden attractors in physical systems described by non-integer order maps.

KW - Discrete fractional calculus

KW - Hardware implementation

KW - chaotic map

UR - https://www.scopus.com/pages/publications/85164538705

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DO - 10.1109/ICFDA58234.2023.10153323

M3 - Conference contribution

AN - SCOPUS:85164538705

T3 - 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

BT - 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

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Ouannas A, Khennaoui AA, Grassi G, Pham VT, Dibi Z, Momani S. Hardware Implementation of a Two-dimensional Fractional Map with Hidden Attractors. In 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023. Institute of Electrical and Electronics Engineers Inc. 2023. (2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023). doi: 10.1109/ICFDA58234.2023.10153323

Hardware Implementation of a Two-dimensional Fractional Map with Hidden Attractors

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