A new 4-D hyperchaotic hidden attractor system: Its dynamics, coexisting attractors, synchronization and microcontroller implementation

Jasim, Basil H.; Hassan, Kadhim H.; Omran, Khulood Moosa

doi:10.11591/ijece.v11i3.pp2068-2078

Cited by 10 publications

(6 citation statements)

References 24 publications

(29 reference statements)

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“…This shows that the 4-D hyperchaotic model (1) has a hidden attractor. [11][12][13] Numerical simulations in MATLAB provide the signal plots of the 4-D hyperchaotic two-scroll system (1), which are plotted in Figure 1.…”

Section: A New Hyperchaotic Two-scroll System With a Hidden Attractormentioning

confidence: 99%

“…Recent research studies show the application of hyperchaotic systems in several engineering areas such as robotics, 1 memristors, 2–4 neural networks, 5,6 encryption, 7,8 and circuits 9,10 . In the hyperchaos literature, there is also a significant interest in developing hyperchaotic systems with no rest points, as such systems are known to possess hidden attractors 11–13 …”

Section: Introductionmentioning

confidence: 99%

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A new 4‐D hyperchaotic two‐scroll system with hidden attractor and its field‐programmable gate array implementation

Vaidyanathan,

Benkouider,

Ovilla‐Martinez

et al. 2023

Circuit Theory & Apps

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SummaryThis research work reports the finding of a new 4‐D hyperchaotic two‐scroll system having three second‐order nonlinear terms. It is detailed that the system does not have any rest point for non‐zero values of the system parameters. Thus, we deduce that the new hyperchaotic system has a hidden attractor. The main findings of the new hyperchaotic system include a detailed bifurcation analysis, coexisting attractors, and offset‐boosting control. The new 4‐D hyperchaotic two‐scroll system with hidden attractor is prototyped using the field‐programmable gate array (FPGA) Zybo Z7‐20 development board, Xilinx Vivado tool, and the hardware description by VHDL. It is highlighted that the simulation of the circuit design, and the experimental results from the FPGA synthesis, all of them are in good agreement with theoretical simulations.

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Section: A New Hyperchaotic Two-scroll System With a Hidden Attractormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A new 4‐D hyperchaotic two‐scroll system with hidden attractor and its field‐programmable gate array implementation

Vaidyanathan,

Benkouider,

Ovilla‐Martinez

et al. 2023

Circuit Theory & Apps

View full text Add to dashboard Cite

show abstract

“…Lyapunov exponents are determined in nonlinear systems and strongly imply that systems exhibit chaotic behaviors [36]. Lyapunov exponents (Lei; i = 1, 2, ...n) are the numbers that show the exponential attraction or time separation of two adjacent orbits in phase space.…”

Section: Lyapunov Exponentmentioning

confidence: 99%

Chaotic Dynamics in the 2D System of Nonsmooth Ordinary Differential Equations

Rahman

Jasim

Al‐Yasir

2022

ijcsm

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Over the last decade, the chaotic behaviors of dynamical systems have been extensively explored. Recently, discovering or developing a 2D system of ordinary differential equations (ODEs) capable of exhibiting chaotic dynamical behaviors is an attractive research topic. In this study, a chaotic system with a 2D system of nonsmooth ODEs has been developed. This system is can exhibit chaotic dynamical behaviors. Its main dynamical behaviors, including time-series trajectories, phase portraits of attractors, and equilibria and their stability, have been investigated. The developed system has been verified by an excessive variety of fascinating chaotic behaviors, such as chaotic attractor, symmetry, sensitivity to initial conditions (ICs), fractal dimension, autocorrelation, power spectrum, Lyapunov exponent, and bifurcation diagram. Analytical and numerical simulations are used to study the dynamical behaviors of such a system. The developed system has extreme sensitivity to ICs, a fractal dimension of more than 1.8 and less than 2.05, an autocorrelation fluctuating randomly about an average of zero, a broadband power spectrum, and one positive Lyapunov exponent. The obtained numerical simulation results have proven the capability of the developed 2D system for exciting chaotic dynamical behaviors

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“…Bifurcation diagrams and Lyapunov exponents are the two basic dynamical tools for investigating the dynamical characteristics of nonlinear chaotic systems [41]. The bifurcation diagrams and Lyapunov exponents are numerically investigated in this section by using MATLAB.…”

Section: Complex Dynamics Of the Systemmentioning

confidence: 99%

High-Security Image Encryption Based on a Novel Simple Fractional-Order Memristive Chaotic System with a Single Unstable Equilibrium Point

et al. 2021

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Fractional-order chaotic systems have more complex dynamics than integer-order chaotic systems. Thus, investigating fractional chaotic systems for the creation of image cryptosystems has been popular recently. In this article, a fractional-order memristor has been developed, tested, numerically analyzed, electronically realized, and digitally implemented. Consequently, a novel simple three-dimensional (3D) fractional-order memristive chaotic system with a single unstable equilibrium point is proposed based on this memristor. This fractional-order memristor is connected in parallel with a parallel capacitor and inductor for constructing the novel fractional-order memristive chaotic system. The system’s nonlinear dynamic characteristics have been studied both analytically and numerically. To demonstrate the chaos behavior in this new system, various methods such as equilibrium points, phase portraits of chaotic attractor, bifurcation diagrams, and Lyapunov exponent are investigated. Furthermore, the proposed fractional-order memristive chaotic system was implemented using a microcontroller (Arduino Due) to demonstrate its digital applicability in real-world applications. Then, in the application field of these systems, based on the chaotic behavior of the memristive model, an encryption approach is applied for grayscale original image encryption. To increase the encryption algorithm pirate anti-attack robustness, every pixel value is included in the secret key. The state variable’s initial conditions, the parameters, and the fractional-order derivative values of the memristive chaotic system are used for contracting the keyspace of that applied cryptosystem. In order to prove the security strength of the employed encryption approach, the cryptanalysis metric tests are shown in detail through histogram analysis, keyspace analysis, key sensitivity, correlation coefficients, entropy analysis, time efficiency analysis, and comparisons with the same fieldwork. Finally, images with different sizes have been encrypted and decrypted, in order to verify the capability of the employed encryption approach for encrypting different sizes of images. The common cryptanalysis metrics values are obtained as keyspace = 2648, NPCR = 0.99866, UACI = 0.49963, H(s) = 7.9993, and time efficiency = 0.3 s. The obtained numerical simulation results and the security metrics investigations demonstrate the accuracy, high-level security, and time efficiency of the used cryptosystem which exhibits high robustness against different types of pirate attacks.

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A new 4-D hyperchaotic hidden attractor system: Its dynamics, coexisting attractors, synchronization and microcontroller implementation

Cited by 10 publications

References 24 publications

A new 4‐D hyperchaotic two‐scroll system with hidden attractor and its field‐programmable gate array implementation

A new 4‐D hyperchaotic two‐scroll system with hidden attractor and its field‐programmable gate array implementation

Chaotic Dynamics in the 2D System of Nonsmooth Ordinary Differential Equations

High-Security Image Encryption Based on a Novel Simple Fractional-Order Memristive Chaotic System with a Single Unstable Equilibrium Point

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