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<p>Discovering simple systems with the minimal number of terms is both rare and challenging. This paper introduces a new, simple five-term dissipative 3D chaotic system derived from a third-order ordinary differential equation (ODE) in a single variable. The system is characterized by a single non-hyperbolic equilibrium point or critical value, with both real eigenvalues equal to zero. The dynamic properties of this system are thoroughly analyzed, including: equilibria points, bifurcation diagram, Lyapunov exponents and NIST test. Moreover, an electronic circuit for this system is designed using Multisim 14.3 software, and the results obtained from Multisim show excellent agreement with those from MATLAB 2021. Finally, image encryption and decryption algorithms rely on the new system are proposed. The effectiveness of these algorithms is validated through statistical analyses, including histograms and correlation analysis. Security tests and experimental results confirm that these encryption and decryption algorithms offer high security and are promising candidates for practical image applications.</p>

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Image encryption and electronic circuit design using a novel five-term 3D chaotic jerk system

  • 期刊论文

  • 发表日期：

    2025年4月21日

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  • Ammar M. Al-Rawi,
  • Saad Fawzi Al-Azzawi

摘要

Discovering simple systems with the minimal number of terms is both rare and challenging. This paper introduces a new, simple five-term dissipative 3D chaotic system derived from a third-order ordinary differential equation (ODE) in a single variable. The system is characterized by a single non-hyperbolic equilibrium point or critical value, with both real eigenvalues equal to zero. The dynamic properties of this system are thoroughly analyzed, including: equilibria points, bifurcation diagram, Lyapunov exponents and NIST test. Moreover, an electronic circuit for this system is designed using Multisim 14.3 software, and the results obtained from Multisim show excellent agreement with those from MATLAB 2021. Finally, image encryption and decryption algorithms rely on the new system are proposed. The effectiveness of these algorithms is validated through statistical analyses, including histograms and correlation analysis. Security tests and experimental results confirm that these encryption and decryption algorithms offer high security and are promising candidates for practical image applications.