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<p>In this paper, a novel hyperchaotic system model is successfully constructed based on a Lorenz-like framework by introducing new state variables. The dynamics of the proposed system are thoroughly investigated through phase diagrams, time series plots, and the computation of Lyapunov exponents and Kaplan-Yorke dimensions. Additionally, the equilibrium point of the system is identified, and its stability is examined. An adaptive synchronous controller is developed utilizing an adaptive control scheme, achieving complete synchronization between two similar chaotic systems, with its theoretical validity demonstrated. Numerical simulations performed using MATLAB confirm the effectiveness of the synchronization strategy. Furthermore, an analogue circuit model of the new hyperchaotic system is designed employing an improved modular design method for chaotic circuits. The hyperchaotic phase trajectory curves resulting from the simulation of the analogue circuit model exhibit consistency with the numerical simulation results, thereby validating the accuracy of the analogue circuit model. To demonstrate the practical application of the proposed hyperchaotic system, an efficient image encryption algorithm is designed, incorporating a three-layer encryption architecture comprising chaotic fusion scrambling, diffusion with a feedback mechanism, and secondary diffusion. The algorithm utilizes an enhanced key derivation function based on SHA-512 hashing with salt to generate secure initial parameters. Performance evaluation conducted on standard test images reveals that the encrypted images achieve information entropy values extremely close to the ideal value of 8 (7.9993 for Mandrill, 7.9972 for House, and 7.9994 for Peppers), demonstrating superior resistance to statistical attacks compared to existing methods. The encryption scheme also exhibits high sensitivity to initial keys and excellent efficiency through parallel computation implementation. This research not only broadens the application of chaotic system theory but also opens new avenues for practical applications in secure communications and image encryption engineering.</p>

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Synchronization, circuit implementation, and a three-layer image encryption scheme for a novel 5D hyperchaotic system

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Yan Zhou,
  • Yujie Guo,
  • Wei Zhang,
  • Peiyan Zhao

摘要

In this paper, a novel hyperchaotic system model is successfully constructed based on a Lorenz-like framework by introducing new state variables. The dynamics of the proposed system are thoroughly investigated through phase diagrams, time series plots, and the computation of Lyapunov exponents and Kaplan-Yorke dimensions. Additionally, the equilibrium point of the system is identified, and its stability is examined. An adaptive synchronous controller is developed utilizing an adaptive control scheme, achieving complete synchronization between two similar chaotic systems, with its theoretical validity demonstrated. Numerical simulations performed using MATLAB confirm the effectiveness of the synchronization strategy. Furthermore, an analogue circuit model of the new hyperchaotic system is designed employing an improved modular design method for chaotic circuits. The hyperchaotic phase trajectory curves resulting from the simulation of the analogue circuit model exhibit consistency with the numerical simulation results, thereby validating the accuracy of the analogue circuit model. To demonstrate the practical application of the proposed hyperchaotic system, an efficient image encryption algorithm is designed, incorporating a three-layer encryption architecture comprising chaotic fusion scrambling, diffusion with a feedback mechanism, and secondary diffusion. The algorithm utilizes an enhanced key derivation function based on SHA-512 hashing with salt to generate secure initial parameters. Performance evaluation conducted on standard test images reveals that the encrypted images achieve information entropy values extremely close to the ideal value of 8 (7.9993 for Mandrill, 7.9972 for House, and 7.9994 for Peppers), demonstrating superior resistance to statistical attacks compared to existing methods. The encryption scheme also exhibits high sensitivity to initial keys and excellent efficiency through parallel computation implementation. This research not only broadens the application of chaotic system theory but also opens new avenues for practical applications in secure communications and image encryption engineering.