Dynamic Analysis and Field-Programmable Gate Array Implementation of a 5D Fractional-Order Memristive Hyperchaotic System with Multiple Coexisting Attractors

On the basis of the chaotic system proposed by Wang et al. in 2023, this paper constructs a 5D fractional-order memristive hyperchaotic system (FOMHS) with multiple coexisting attractors through coupling of magnetic control memristors and dimension expansion. Firstly, the divergence, Kaplan–Yorke di...

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Published in:Fractal and fractional Vol. 8; no. 5; p. 271
Main Authors: Yu, Fei, Zhang, Wuxiong, Xiao, Xiaoli, Yao, Wei, Cai, Shuo, Zhang, Jin, Wang, Chunhua, Li, Yi
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.05.2024
Subjects:
Behavior
Calculus
Chaos theory
Circuits
coexisting attractors
Decomposition
Differential equations
Digital integrated circuits
Dynamic characteristics
Eigenvalues
Equilibrium
Field programmable gate arrays
FPGA
fractional-order memristive hyperchaotic system
Liapunov exponents
Magnetic control
memristor
Neural networks
Operators (mathematics)
Phase diagrams
ISSN:2504-3110, 2504-3110
Online Access:Get full text
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Summary:On the basis of the chaotic system proposed by Wang et al. in 2023, this paper constructs a 5D fractional-order memristive hyperchaotic system (FOMHS) with multiple coexisting attractors through coupling of magnetic control memristors and dimension expansion. Firstly, the divergence, Kaplan–Yorke dimension, and equilibrium stability of the chaotic model are studied. Subsequently, we explore the construction of the 5D FOMHS, introducing the definitions of the Caputo differential operator and the Riemann–Liouville integral operator and employing the Adomian resolving approach to decompose the linears, the nonlinears, and the constants of the system. The complex dynamic characteristics of the system are analyzed by phase diagrams, Lyapunov exponent spectra, time-domain diagrams, etc. Finally, the hardware circuit of the proposed 5D FOMHS is performed by FPGA, and its randomness is verified using the NIST tool.
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ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract8050271