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

Yu, Fei; Zhang, Wuxiong; Xiao, Xiaoli; Yao, Wei; Cai, Shuo; Zhang, Jin; Wang, Chunhua; Li, Yi

doi:10.3390/fractalfract8050271

Cited by 3 publications

(1 citation statement)

References 54 publications

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“…The study of coexisting attractors has received significant attention in recent years [31][32][33][34][35]. These attractors are increasingly being employed in encryption applications to enhance information security and reduce the risk of decoding [36,37].…”

Section: Introductionmentioning

confidence: 99%

Autonomous three-dimensional oscillator with two and four wings attractors embedded in the microcontroller: analysis, amplitude controls, random number generator, and image encryption application

Alexander,

Emin,

Ngongiah

et al. 2024

Phys. Scr.

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Robust chaotic systems offer unpredictability, complex dynamics, noise-like properties, efficient bifurcation behavior, and the ability to model real-world phenomena, making them valuable in diverse scientific and engineering applications. This paper details on the dynamical appraisal, amplitude controls, microcontroller execution, Random number generator (RNG) of an autonomous three-dimensional (3D) oscillator with two and four wings attractors (ATDOTFWA), and its image encryption application. Thanks to the Routh-Hurwitz criteria, five steady states found in the ATDOTFWA are classified as stable or unstable, depending on its two control parameters. During the numerical simulations employing the Runge-Kutta scheme, the ATDOTFWA exhibit a wide range of dynamic behaviors, including no oscillations, Hopf bifurcation, limit cycle, five distinct presentations of two wings chaotic structures, monostable and bistable two wings chaotic structures, bistable and monostable regular oscillations, chaotic bursting characteristics, coexistence of period-2-oscillations and four wings chaotic structure, and four wings chaotic attractor which were validated experimentally by the microcontroller implementation. The total and partial controls of the amplitude are achieved in the ATDOTFWA. A RNG is designed based on the ATDOTFWA, and the generated random numbers are successfully tested using the ENT and NIST 800-22 statistical test suites, demonstrating the reliability of the ATDOTFWA-based RNG. This reliability is further confirmed through the application of the ATDOTFWA-based RNG in an efficient and secure image encryption process, where the generated random numbers are used as the encryption key. The effectiveness of the image encryption process is validated through comprehensive cryptanalysis, with an encryption time of 0.1923 s for a 512×512 image, an average normalized pixel change rate (NPCR) of 99.6126%, an average unified average changing intensity (UACI) of 33.4578%, and an average information entropy of 7.9994.

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Section: Introductionmentioning

confidence: 99%

Autonomous three-dimensional oscillator with two and four wings attractors embedded in the microcontroller: analysis, amplitude controls, random number generator, and image encryption application

Alexander,

Emin,

Ngongiah

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

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Dynamic Analysis, Image Encryption Application and FPGA Implementation of a Discrete Memristor-Coupled Neural Network

Yu,

Xu,

Lin

et al. 2024

Int. J. Bifurcation Chaos

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This paper presents a novel discrete memristor model that incorporates exponential and absolute value functions. A discrete coupled memristor neural network model is constructed based on this memristor design. The periodic and chaotic regions of the discrete neural network model are determined using bifurcation and Lyapunov exponent spectrum. Furthermore, by varying the initial values of the discrete memristive neural network, we observe the coexistence of chaos and periodic attractors, as well as periodic attractors. Additionally, an application to color image encryption based on the discrete system model is given. Security analysis is conducted in the aspects of key space, histogram analysis, correlation analysis, sensitivity analysis, Peak Signal-to-Noise Ratio (PSNR), and information entropy analysis. The analysis results show that the algorithm has a key space size of [Formula: see text], and the information entropy of baboon graph is 7.9993, which is very close to the ideal value of 8. It shows that the image encryption algorithm is feasible and effective. Finally, the implementation of the discrete memristive neural network model is realized using Field Programmable Gate Array (FPGA). The experimental implementation is conducted using the Verilog language on the Vivado 2018.3 platform, and the obtained results align with the numerical simulation results obtained through MATLAB.

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Design and Analysis of a Novel Fractional-Order System with Hidden Dynamics, Hyperchaotic Behavior and Multi-Scroll Attractors

Yu,

Xu,

Lin

et al. 2024

Mathematics

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The design of chaotic systems with complex dynamic behaviors has always been a key aspect of chaos theory in engineering applications. This study introduces a novel fractional-order system characterized by hidden dynamics, hyperchaotic behavior, and multi-scroll attractors. By employing fractional calculus, the system’s order is extended beyond integer values, providing a richer dynamic behavior. The system’s hidden dynamics are revealed through detailed numerical simulations and theoretical analysis, demonstrating complex attractors and bifurcations. The hyperchaotic nature of the system is verified through Lyapunov exponents and phase portraits, showing multiple positive exponents that indicate a higher degree of unpredictability and complexity. Additionally, the system’s multi-scroll attractors are analyzed, showcasing their potential for secure communication and encryption applications. The fractional-order approach enhances the system’s flexibility and adaptability, making it suitable for a wide range of practical uses, including secure data transmission, image encryption, and complex signal processing. Finally, based on the proposed fractional-order system, we designed a simple and efficient medical image encryption scheme and analyzed its security performance. Experimental results validate the theoretical findings, confirming the system’s robustness and effectiveness in generating complex chaotic behaviors.

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

Cited by 3 publications

References 54 publications

Autonomous three-dimensional oscillator with two and four wings attractors embedded in the microcontroller: analysis, amplitude controls, random number generator, and image encryption application

Autonomous three-dimensional oscillator with two and four wings attractors embedded in the microcontroller: analysis, amplitude controls, random number generator, and image encryption application

Dynamic Analysis, Image Encryption Application and FPGA Implementation of a Discrete Memristor-Coupled Neural Network

Design and Analysis of a Novel Fractional-Order System with Hidden Dynamics, Hyperchaotic Behavior and Multi-Scroll Attractors

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