FPGA-Based Implementation of a New 3-D Multistable Chaotic Jerk System with Two Unstable Balance Points

Vaidyanathan, Sundarapandian; Tlelo‐Cuautle, Esteban; Benkouider, Khaled; Sambas, Aceng; Ovilla-Martínez, Brisbane

doi:10.3390/technologies11040092

Cited by 3 publications

(1 citation statement)

References 34 publications

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“…This implies that any perturbation introduced into the system will amplify over time, leading to a loss of stability at the equilibrium point. Conversely, the remaining five eigenvalues exhibit negative real components, indicating that any disturbance introduced into the system will gradually diminish, thereby preserving the stability of the equilibrium point [26].…”

Section: Dimension and Lyapunovmentioning

confidence: 99%

A Novel Eighth-Order Hyperchaotic System and Its Application in Image Encryption

Qiu,

Zhang,

Yue

et al. 2023

Mathematics

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With the advancement in information and communication technologies (ICTs), the widespread dissemination and sharing of digital images has raised concerns regarding privacy and security. Traditional methods of encrypting images often suffer from limitations such as a small key space and vulnerability to brute-force attacks. To address these issues, this paper proposes a novel eighth-order hyperchaotic system. This hyperchaotic system exhibits various dynamic behaviors, including hyperchaos, sub-hyperchaos, and chaos. The encryption scheme based on this system offers a key space larger than 22338. Through a comprehensive analysis involving histogram analysis, key space analysis, correlation analysis, entropy analysis, key sensitivity analysis, differential attack analysis, and cropping attack analysis, it is demonstrated that the proposed system is capable of resisting statistical attacks, brute force attacks, differential attacks, and cropping attacks, thereby providing excellent security performance.

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Section: Dimension and Lyapunovmentioning

confidence: 99%

A Novel Eighth-Order Hyperchaotic System and Its Application in Image Encryption

Qiu,

Zhang,

Yue

et al. 2023

Mathematics

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A New Hyperjerk System With a Half Line Equilibrium: Multistability, Period Doubling Reversals, Antimonotonocity, Electronic Circuit, FPGA Design, and an Application to Image Encryption

Sambas,

Miroslav,

Vaidyanathan

et al. 2024

IEEE Access

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A hyperjerk system pertains to a dynamical system regulated by an ordinary differential equation of nth order, where n ≥ 4. The main contribution of this work is the finding of a new autonomous hyperjerk system with a half line equilibrium. The mathematical framework of the proposed hyperjerk system contains eight terms with an absolute function nonlinearity. The essential dynamic characteristics of the model are explored, encompassing analysis of equilibrium points and their stability, depiction of the phase trajectories, illustration of bifurcation patterns, and visualization of Lyapunov exponent graphs. Our finding shows that the new 4D hyperjerk system exhibits special behavior like multistability, period doubling reversals and antimonotonocity. The proposed hyperjerk system has been implemented with an electronic circuit using MultiSim 14.0. Moreover, the FPGA implementation of the proposed hyperjerk system is performed by applying two numerical methods: Forward Euler and Trapezoidal. Experimental attractors are given from an oscilloscope by using the Zybo Z7-20 FPGA development board, which are in good agreement with the MATLAB and MultiSim 14.0 simulations. Finally, based on the chaotic dynamical behavior of the proposed chaotic hyperjerk system, a new image encryption approach is proposed. The experimental outcomes of the presented encryption algorithm prove its efficiency and security.

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The Reinartz Oscillator: Analysis Beyond Regular Behavior of the Circuit

Petrzela,

Kaller,

Vavra

2024

IEEE Access

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This paper is focused on nonlinear behavior associated with fourth-order autonomous lumped circuit known as the Reinartz oscillator. It is shown that this naturally sinusoidal oscillator with three-winding transformer can exhibit robust chaotic behavior. Essential scalar polynomial nonlinearity is not intrinsic to transformer, but to active two-port element described by impedance parameters. The existence of complex solutions is proved on numerical as well as experimental basis. In the first case, conventional routines for qualitative analysis of dynamical flows were applied, based on either prescribed set of differential equations or generated data sequence. In detail, a pair of the largest Lyapunov exponents are visualized with respect to key system parameters, attractor dimensions, recurrence plots and bifurcation diagrams showing interesting routes-to-chaos scenarios are provided to illustrate complexity of observed steady state motion. For the second case, electronic circuits dynamically equivalent to investigated mathematical model will be designed, constructed, and experimentally measured. Chaotic signals captured as oscilloscope screenshots will be compared to theoretical counterparts.

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FPGA-Based Implementation of a New 3-D Multistable Chaotic Jerk System with Two Unstable Balance Points

Cited by 3 publications

References 34 publications

A Novel Eighth-Order Hyperchaotic System and Its Application in Image Encryption

A Novel Eighth-Order Hyperchaotic System and Its Application in Image Encryption

A New Hyperjerk System With a Half Line Equilibrium: Multistability, Period Doubling Reversals, Antimonotonocity, Electronic Circuit, FPGA Design, and an Application to Image Encryption

The Reinartz Oscillator: Analysis Beyond Regular Behavior of the Circuit

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