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<p>High-dimensional chaotic maps offer greater advantages in applications compared to low-dimensional chaotic maps; yet, developing methods to generate <i>n</i>-dimensional chaotic maps is a significant challenge. This work introduces two methods for creating <i>n</i>-dimensional hyperchaotic maps (<i>n</i>D-HCM) using strictly diagonal explicit real symmetric matrices. The results demonstrate that the <i>n</i>D-HCM created with the proposed methods shows complex and controllable chaotic behavior. Concurrently, using suitable system parameters and control parameters, the <i>n</i>D-HCM exhibits intricate dynamical behavior caused by several elements and generates homogeneous and heterogeneous attractors. Furthermore, all state variables of <i>n</i>D-HCM may successfully pass the NIST test when compared with similar current maps. An FPGA-based experimental platform has been built for running <i>n</i>D-HCM in only 8 calculation cycles for each iteration by employing the fixed-point criterion. Ultimately, <i>n</i>D-HCM is employed in a pseudo-random generator (PRNG) whose throughput rate is 3.6 Gbps, and apply the chaos-based PRNG as additive noise in direct digital synthesis (DDS)-based waveform generator to address the short-period issue of noise, thereby generating noise-containing waveforms with adjustable signal-to-noise ratio (SNR).</p>

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Design and FPGA implementation of n-dimensional hyperchaotic maps using strictly diagonal-dominant real symmetric matrices: applications in additive noise generation

  • 期刊论文

  • 发表日期：

    2026年2月3日

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  • Wei Shi,
  • Jia Zhao,
  • Yuchuan Guo,
  • Jiajv Li,
  • Fenghao Zhong,
  • Bo Xu

摘要

High-dimensional chaotic maps offer greater advantages in applications compared to low-dimensional chaotic maps; yet, developing methods to generate n-dimensional chaotic maps is a significant challenge. This work introduces two methods for creating n-dimensional hyperchaotic maps (nD-HCM) using strictly diagonal explicit real symmetric matrices. The results demonstrate that the nD-HCM created with the proposed methods shows complex and controllable chaotic behavior. Concurrently, using suitable system parameters and control parameters, the nD-HCM exhibits intricate dynamical behavior caused by several elements and generates homogeneous and heterogeneous attractors. Furthermore, all state variables of nD-HCM may successfully pass the NIST test when compared with similar current maps. An FPGA-based experimental platform has been built for running nD-HCM in only 8 calculation cycles for each iteration by employing the fixed-point criterion. Ultimately, nD-HCM is employed in a pseudo-random generator (PRNG) whose throughput rate is 3.6 Gbps, and apply the chaos-based PRNG as additive noise in direct digital synthesis (DDS)-based waveform generator to address the short-period issue of noise, thereby generating noise-containing waveforms with adjustable signal-to-noise ratio (SNR).