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<p>This paper presents a piecewise Duffing map (PDM) model that introduces piecewise nonlinearity to the classic Duffing map and explores its rich dynamical behaviour, including bistable periodic oscillations, bistable periodic doubling and bistable<InlineEquation ID="IEq1000"> <EquationSource Format="TEX">\(/\)</EquationSource> <EquationSource Format="MATHML"><math> <mo stretchy="false">/</mo> </math></EquationSource> </InlineEquation>monostable chaotic characteristics. By incorporating two constant parameters in the PDM’s rate equations, the authors demonstrate the ability to flexibly control the amplitude of the chaotic sequences, with total amplitude control achieved by introducing an additional parameter. The dynamical characteristics of the PDM are validated through microcontroller implementation and the chaotic properties of the PDM are leveraged to develop a pseudo-random number generator (PRNG) with a linear feedback shift register (LFSR) as a post-processing unit. The randomness of the generated binary data is extensively tested using the NIST 800-22 test suite, confirming the suitability of the PDM-based PRNG for applications such as secure communication schemes and other chaos-based applications.</p>

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Piecewise Duffing map embedded in the microcontroller: dynamical probing and pseudo-random number generation

  • 期刊论文

  • 发表日期：

    2025年11月20日

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  • Parvathyshankar Deiva Sundari,
  • Rolande Tsapla Fotsa,
  • Isidore Komofor Ngongiah,
  • André Chéagé Chamgoué,
  • Karthikeyan Rajagopal

摘要

This paper presents a piecewise Duffing map (PDM) model that introduces piecewise nonlinearity to the classic Duffing map and explores its rich dynamical behaviour, including bistable periodic oscillations, bistable periodic doubling and bistable \(/\) / monostable chaotic characteristics. By incorporating two constant parameters in the PDM’s rate equations, the authors demonstrate the ability to flexibly control the amplitude of the chaotic sequences, with total amplitude control achieved by introducing an additional parameter. The dynamical characteristics of the PDM are validated through microcontroller implementation and the chaotic properties of the PDM are leveraged to develop a pseudo-random number generator (PRNG) with a linear feedback shift register (LFSR) as a post-processing unit. The randomness of the generated binary data is extensively tested using the NIST 800-22 test suite, confirming the suitability of the PDM-based PRNG for applications such as secure communication schemes and other chaos-based applications.