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<p>In this paper, a new discrete memristor based on the combination of Sigmoid and Sinusoidal functions is proposed and a generalized two-dimensional discrete memristor(2D-DM) mapping model is constructed. The model retains the graphical structure and characterization of the seed function while significantly enhancing the chaotic complexity by combining the discrete memristor with the classical seed function. On this basis, four representative two-dimensional hyperchaotic maps are generated. Simulation and theoretical analysis show that these maps can generate hyperchaotic attractors with highly similar morphology to the corresponding seed functions under different control parameters, and exhibit periodic bifurcation, multiple stability, and high-dimensional hyperchaotic behavior. The pseudo-random number generator constructed based on mapped output has been tested by NIST for good randomness. Finally, in this paper, 2D-DM mapping is implemented on digital circuits to verify its feasibility. The proposed model provides new ideas for controllable attractor morphology design and high-quality pseudo-random sequence generation. These properties are essential for applications including chaotic encryption, secure communication, and reservoir computing.</p>

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Memristor-based hyperchaotic maps of attractors with nonlinear term-like graphs and their hardware implementation

  • 期刊论文

  • 发表日期：

    2025年9月25日

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  • Xiaosheng Feng,
  • Tingkai Zhao,
  • Yuke Tang,
  • Yuqi Wei,
  • Baoxiang Du

摘要

In this paper, a new discrete memristor based on the combination of Sigmoid and Sinusoidal functions is proposed and a generalized two-dimensional discrete memristor(2D-DM) mapping model is constructed. The model retains the graphical structure and characterization of the seed function while significantly enhancing the chaotic complexity by combining the discrete memristor with the classical seed function. On this basis, four representative two-dimensional hyperchaotic maps are generated. Simulation and theoretical analysis show that these maps can generate hyperchaotic attractors with highly similar morphology to the corresponding seed functions under different control parameters, and exhibit periodic bifurcation, multiple stability, and high-dimensional hyperchaotic behavior. The pseudo-random number generator constructed based on mapped output has been tested by NIST for good randomness. Finally, in this paper, 2D-DM mapping is implemented on digital circuits to verify its feasibility. The proposed model provides new ideas for controllable attractor morphology design and high-quality pseudo-random sequence generation. These properties are essential for applications including chaotic encryption, secure communication, and reservoir computing.