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<p>Considering the challenges of discrete memristor (DM) models in representing delay phenomena during charge transfer and reception in real memristors, we propose a general discrete time-delay memristor (DTDM) model. Taking four memristance nonlinearities as examples, we verify that the DTDMs belong to the category of generalized memristors. Based on these models, four DTDM chaotic maps are designed by using a simple self-feedback method. The simulation results show that they have complex phase space trajectories, hidden attractors, hyperchaotic behavior, coexisting attractors, and initial-boosting behavior. Furthermore, the DTDM maps show a broader initials-relied chaotic range than their original DM maps. Especially in implicit oscillation scenarios, they exhibit superior anti-degradation ability and lower autocorrelation, while maintaining a similar permutation entropy (PE) complexity. Finally, four DTDM models and their corresponding chaotic maps are realized on field-programmable gate array (FPGA), and these maps are applied to pseudorandom number generators (PRNG) and compressive sensing (CS).</p>

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Discrete Time-Delay Memristive Chaotic Map and Its Applications

  • 期刊论文

  • 发表日期：

    2025年8月21日

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  • Wenhao Liu,
  • Kehui Sun,
  • Huihai Wang,
  • Jin Liu

摘要

Considering the challenges of discrete memristor (DM) models in representing delay phenomena during charge transfer and reception in real memristors, we propose a general discrete time-delay memristor (DTDM) model. Taking four memristance nonlinearities as examples, we verify that the DTDMs belong to the category of generalized memristors. Based on these models, four DTDM chaotic maps are designed by using a simple self-feedback method. The simulation results show that they have complex phase space trajectories, hidden attractors, hyperchaotic behavior, coexisting attractors, and initial-boosting behavior. Furthermore, the DTDM maps show a broader initials-relied chaotic range than their original DM maps. Especially in implicit oscillation scenarios, they exhibit superior anti-degradation ability and lower autocorrelation, while maintaining a similar permutation entropy (PE) complexity. Finally, four DTDM models and their corresponding chaotic maps are realized on field-programmable gate array (FPGA), and these maps are applied to pseudorandom number generators (PRNG) and compressive sensing (CS).