FPGA Implementation of Fractional-Order Chaotic Systems

Mohammed F. Tolba; Amr M. AbdelAty; Lobna A. Said; Ahmed H. Madian; Ahmed G. Radwan

doi:10.1016/B978-0-12-816152-4.00002-9

FPGA Implementation of Fractional-Order Chaotic Systems

Mohammed F. Tolba, Amr M. AbdelAty, Lobna A. Said, Ahmed H. Madian, Ahmed G. Radwan

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

4 Scopus citations

Abstract

This chapter introduces two FPGA implementations of the fractional-order operators: the Caputo and the Grünwald-Letnikov (GL) derivatives. First, the Caputo derivative is realized using nonuniform segmentation to reduce the size of the Look-Up Table. The Caputo implementation introduced can generate derivatives of previously defined functions only. Generic and complete hardware architecture of the GL operator is realized with different memory window sizes. The generic architecture is used as a block to implement several fractional-order chaotic systems. The investigated systems include Borah, Chen, Liu, Li, and Arneodo fractional-order chaotic systems. Different interesting attractors are realized under various parametric changes with distinct step sizes for different fractional orders. To verify the chaotic behavior of the generated attractors, the Maximum Lyapunov Exponent is calculated for each system at different parameter values.

Original language	British English
Title of host publication	Fractional Order Systems
Subtitle of host publication	Optimization, Control, Circuit Realizations and Applications
Publisher	Elsevier
Pages	33-62
Number of pages	30
ISBN (Electronic)	9780128161524
ISBN (Print)	9780128163085
DOIs	https://doi.org/10.1016/B978-0-12-816152-4.00002-9
State	Published - 1 Jan 2018

Keywords

Chaotic system
FPGA
Fractional order
Liu system
Multiscroll
V-shape

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10.1016/B978-0-12-816152-4.00002-9

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title = "FPGA Implementation of Fractional-Order Chaotic Systems",

abstract = "This chapter introduces two FPGA implementations of the fractional-order operators: the Caputo and the Gr{\"u}nwald-Letnikov (GL) derivatives. First, the Caputo derivative is realized using nonuniform segmentation to reduce the size of the Look-Up Table. The Caputo implementation introduced can generate derivatives of previously defined functions only. Generic and complete hardware architecture of the GL operator is realized with different memory window sizes. The generic architecture is used as a block to implement several fractional-order chaotic systems. The investigated systems include Borah, Chen, Liu, Li, and Arneodo fractional-order chaotic systems. Different interesting attractors are realized under various parametric changes with distinct step sizes for different fractional orders. To verify the chaotic behavior of the generated attractors, the Maximum Lyapunov Exponent is calculated for each system at different parameter values.",

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AU - Tolba, Mohammed F.

AU - AbdelAty, Amr M.

AU - Said, Lobna A.

AU - Madian, Ahmed H.

AU - Radwan, Ahmed G.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - This chapter introduces two FPGA implementations of the fractional-order operators: the Caputo and the Grünwald-Letnikov (GL) derivatives. First, the Caputo derivative is realized using nonuniform segmentation to reduce the size of the Look-Up Table. The Caputo implementation introduced can generate derivatives of previously defined functions only. Generic and complete hardware architecture of the GL operator is realized with different memory window sizes. The generic architecture is used as a block to implement several fractional-order chaotic systems. The investigated systems include Borah, Chen, Liu, Li, and Arneodo fractional-order chaotic systems. Different interesting attractors are realized under various parametric changes with distinct step sizes for different fractional orders. To verify the chaotic behavior of the generated attractors, the Maximum Lyapunov Exponent is calculated for each system at different parameter values.

AB - This chapter introduces two FPGA implementations of the fractional-order operators: the Caputo and the Grünwald-Letnikov (GL) derivatives. First, the Caputo derivative is realized using nonuniform segmentation to reduce the size of the Look-Up Table. The Caputo implementation introduced can generate derivatives of previously defined functions only. Generic and complete hardware architecture of the GL operator is realized with different memory window sizes. The generic architecture is used as a block to implement several fractional-order chaotic systems. The investigated systems include Borah, Chen, Liu, Li, and Arneodo fractional-order chaotic systems. Different interesting attractors are realized under various parametric changes with distinct step sizes for different fractional orders. To verify the chaotic behavior of the generated attractors, the Maximum Lyapunov Exponent is calculated for each system at different parameter values.

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KW - FPGA

KW - Fractional order

KW - Liu system

KW - Multiscroll

KW - V-shape

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FPGA Implementation of Fractional-Order Chaotic Systems

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