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<p>This study introduces a novel 4D conformable fractional-order ecological system designed to generate hyperchaotic dynamics for secure image encryption. We derive the numerical solution using the Conformable Adomian Decomposition Method (CADM), which provides efficient computation of fractional-order dynamics. Comprehensive dynamical analysis reveals that the system exhibits rich behaviors, including periodic orbits, chaos, and hyperchaos, depending on parameter variations and fractional order. Two positive Lyapunov exponents confirm hyperchaotic characteristics, while bifurcation diagrams and phase portraits illustrate the system’s complex nonlinear behavior. Building upon these dynamics, we achieve Modified Generalized Projective Synchronization (MGPS) between two identical fractional-order systems using a nonlinear control scheme based on fractional stability theory. Leveraging the synchronized hyperchaotic signals, we develop a robust image encryption algorithm that combines multi-dimensional permutation and diffusion processes. The encryption scheme utilizes a 17-dimensional key space for enhanced security and demonstrates resistance against statistical, differential, and chosen-plaintext attacks. Experimental results on standard grayscale images confirm excellent performance with near-ideal entropy (7.9993), near-zero correlation coefficients, and high sensitivity to key variations. The proposed cryptosystem also shows strong robustness against noise and cropping attacks. This work bridges fractional-order ecological modeling with practical cryptographic applications, offering a secure and efficient framework for digital image protection.</p>

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Fractional-order Modeling of Ecological Interactions with Hyperchaotic Dynamics for Secure Image Encryption

  • 期刊论文

  • 发表日期：

    2026年3月14日

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  • Haneche Nabil,
  • Hamaizia Tayeb

摘要

This study introduces a novel 4D conformable fractional-order ecological system designed to generate hyperchaotic dynamics for secure image encryption. We derive the numerical solution using the Conformable Adomian Decomposition Method (CADM), which provides efficient computation of fractional-order dynamics. Comprehensive dynamical analysis reveals that the system exhibits rich behaviors, including periodic orbits, chaos, and hyperchaos, depending on parameter variations and fractional order. Two positive Lyapunov exponents confirm hyperchaotic characteristics, while bifurcation diagrams and phase portraits illustrate the system’s complex nonlinear behavior. Building upon these dynamics, we achieve Modified Generalized Projective Synchronization (MGPS) between two identical fractional-order systems using a nonlinear control scheme based on fractional stability theory. Leveraging the synchronized hyperchaotic signals, we develop a robust image encryption algorithm that combines multi-dimensional permutation and diffusion processes. The encryption scheme utilizes a 17-dimensional key space for enhanced security and demonstrates resistance against statistical, differential, and chosen-plaintext attacks. Experimental results on standard grayscale images confirm excellent performance with near-ideal entropy (7.9993), near-zero correlation coefficients, and high sensitivity to key variations. The proposed cryptosystem also shows strong robustness against noise and cropping attacks. This work bridges fractional-order ecological modeling with practical cryptographic applications, offering a secure and efficient framework for digital image protection.