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<p>Iterated maps play a vital role in nonlinear models, attracting interest from various fields. Despite progress in understanding iterated trajectories, many simple maps lack comprehensive analysis. The cube map is favored for minimal distortion, but still faces geometric issues that affect motion compensation quality. Addressing these distortions could enhance coding efficiency and improve applications in complex systems. The dynamical probing, microcontroller execution, and sound steganography in a piecewise quadratic map with absolute nonlinearity (QMAN) brought about by substituting the cubic term in the cubic map by piecewise nonlinearity is investigated in this paper. The QMAN has an inversion symmetry and one or three steady states, characterized by its parameters, as well as the stability of steady states. The numerical simulations of QMAN reveal bistable regular attractors, evolution of bistable periodic-2 oscillations to bistable and monostable chaotic attractors. The amplitude of QMAN is controlled by introducing a constant parameter in the QMAN’s differential map. The dynamical characteristics are realized by the microcontroller validation scheme. QMAN demonstrates its secure applicability in scientific fields such as data security and data hiding through the implementation of a sound steganography application based on the least significant bit (LSB) method. The reliability of the steganography application is validated through comprehensive analyses, including peak signal-to-noise ratio (PSNR), mean square error (MSE), signal-to-noise ratio (SNR), embedding rate (ER), waveform, spectrogram, hiding capacity (HC), histogram, and percentage root means square difference (PRD). It is proven that the proposed scheme can be successfully employed in secure sound communication applications.</p>

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Absolute-Value Quadratic Map Embedded in the Microcontroller: Dynamical Analysis and Sound Steganography

  • 期刊论文

  • 发表日期：

    2026年8月1日

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  • Parvathyshankar Deiva Sundari,
  • Berkay Emin,
  • Rolande Tsapla Fotsa,
  • Cyrille Ainamon,
  • Akif Akgül,
  • Karthikeyan Rajagopal

摘要

Iterated maps play a vital role in nonlinear models, attracting interest from various fields. Despite progress in understanding iterated trajectories, many simple maps lack comprehensive analysis. The cube map is favored for minimal distortion, but still faces geometric issues that affect motion compensation quality. Addressing these distortions could enhance coding efficiency and improve applications in complex systems. The dynamical probing, microcontroller execution, and sound steganography in a piecewise quadratic map with absolute nonlinearity (QMAN) brought about by substituting the cubic term in the cubic map by piecewise nonlinearity is investigated in this paper. The QMAN has an inversion symmetry and one or three steady states, characterized by its parameters, as well as the stability of steady states. The numerical simulations of QMAN reveal bistable regular attractors, evolution of bistable periodic-2 oscillations to bistable and monostable chaotic attractors. The amplitude of QMAN is controlled by introducing a constant parameter in the QMAN’s differential map. The dynamical characteristics are realized by the microcontroller validation scheme. QMAN demonstrates its secure applicability in scientific fields such as data security and data hiding through the implementation of a sound steganography application based on the least significant bit (LSB) method. The reliability of the steganography application is validated through comprehensive analyses, including peak signal-to-noise ratio (PSNR), mean square error (MSE), signal-to-noise ratio (SNR), embedding rate (ER), waveform, spectrogram, hiding capacity (HC), histogram, and percentage root means square difference (PRD). It is proven that the proposed scheme can be successfully employed in secure sound communication applications.