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<p>Variable-order differential operators can be useful for modeling chaotical systems and nonlinear. This paper introduces a novel discrete fractional-order <i>q</i>-deformed Stefanski map and investigates its dynamical properties, stability, synchronization, and cryptographic applications. The study begins the incorporation of <i>q</i>-deformation and fractional-order dynamics. The proposed system’s complex behavior is analyzed using the Lyapunov exponent, entropy analysis, bifurcation diagrams, phase plots, time history plots, and the 0-1 test, revealing various attractors, including chaotic, quasi-periodic, and non-chaotic states. These findings highlight the map’s enhanced complexity and potential for diverse applications. A detailed chaos analysis is also performed, showcasing the strengthened unpredictability and sensitivity of the <i>q</i>-deformed Stefanski map. Stability and synchronization are explored using adaptive control techniques, demonstrating their effectiveness in regulating chaotic behavior. Furthermore, the study uses the chaotic properties of the system to develop a robust image encryption scheme. The encryption framework integrates permutation and diffusion mechanisms, ensuring enhanced security and resistance against statistical and differential attacks. Comparative analysis confirms the superiority of the proposed encryption approach over traditional methods.</p>

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Dynamical analysis, stabilization, and synchronization in the q-deformed discrete fractional Stefanski map

  • 期刊论文

  • 发表日期：

    2025年5月3日

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  • M. G. Abbas Malik,
  • Muhammad Awais,
  • Irfan Ullah,
  • Zia Bashir

摘要

Variable-order differential operators can be useful for modeling chaotical systems and nonlinear. This paper introduces a novel discrete fractional-order q-deformed Stefanski map and investigates its dynamical properties, stability, synchronization, and cryptographic applications. The study begins the incorporation of q-deformation and fractional-order dynamics. The proposed system’s complex behavior is analyzed using the Lyapunov exponent, entropy analysis, bifurcation diagrams, phase plots, time history plots, and the 0-1 test, revealing various attractors, including chaotic, quasi-periodic, and non-chaotic states. These findings highlight the map’s enhanced complexity and potential for diverse applications. A detailed chaos analysis is also performed, showcasing the strengthened unpredictability and sensitivity of the q-deformed Stefanski map. Stability and synchronization are explored using adaptive control techniques, demonstrating their effectiveness in regulating chaotic behavior. Furthermore, the study uses the chaotic properties of the system to develop a robust image encryption scheme. The encryption framework integrates permutation and diffusion mechanisms, ensuring enhanced security and resistance against statistical and differential attacks. Comparative analysis confirms the superiority of the proposed encryption approach over traditional methods.