Scholarlink

<p>Discrete memristors (DMs) have gained significant attention for their ability to enhance the complexity of simple chaotic maps, primarily due to their inherent nonlinearity. Despite their widespread application in this context, the intrinsic chaotic properties of DMs remain underexplored. In this paper, we incorporate an ingenious oscillatory term into the DM model, thereby constructing three novel hyperchaotic maps. These maps achieve ultra-high Lyapunov exponents (LEs), significantly surpassing typical ranges (0-0.5) in prior 2D memristive systems. The integration of this oscillatory term elevates dynamical complexity, revealing hyperchaotic dynamics with coexisting multiple attractors and diverse multi-pulse discharge modes. Furthermore, these maps are implemented on a field-programmable gate array (FPGA) platform, and the Structural Similarity Index (SSIM &gt; 0.9) and Mean Square Error (MSE &lt; 0.0005) metrics obtained confirmed the effectiveness of the FPGA implementation scheme. Additionally, pseudorandom number generators (PRNGs) based on these maps pass all 15 NIST SP800-22 tests, demonstrating their applicability in secure communications. This exploration of discrete memristive maps not only enriches the understanding of memristor-based chaotic systems but also establishes a foundational framework for future investigations into the design and optimization of memristive maps, thereby fostering further innovation in this burgeoning field.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Discrete memristive hyperchaotic maps with high Lyapunov exponents

  • 期刊论文

  • 发表日期：

    2025年7月14日

查看全文
  • Dingwei Luo,
  • Chunhua Wang,
  • Quanli Deng,
  • Gang Yang

摘要

Discrete memristors (DMs) have gained significant attention for their ability to enhance the complexity of simple chaotic maps, primarily due to their inherent nonlinearity. Despite their widespread application in this context, the intrinsic chaotic properties of DMs remain underexplored. In this paper, we incorporate an ingenious oscillatory term into the DM model, thereby constructing three novel hyperchaotic maps. These maps achieve ultra-high Lyapunov exponents (LEs), significantly surpassing typical ranges (0-0.5) in prior 2D memristive systems. The integration of this oscillatory term elevates dynamical complexity, revealing hyperchaotic dynamics with coexisting multiple attractors and diverse multi-pulse discharge modes. Furthermore, these maps are implemented on a field-programmable gate array (FPGA) platform, and the Structural Similarity Index (SSIM > 0.9) and Mean Square Error (MSE < 0.0005) metrics obtained confirmed the effectiveness of the FPGA implementation scheme. Additionally, pseudorandom number generators (PRNGs) based on these maps pass all 15 NIST SP800-22 tests, demonstrating their applicability in secure communications. This exploration of discrete memristive maps not only enriches the understanding of memristor-based chaotic systems but also establishes a foundational framework for future investigations into the design and optimization of memristive maps, thereby fostering further innovation in this burgeoning field.