A Fractional-Order Memristor-Based Autapse Hopfield Neural Network: Nonlinear Dynamics Analysis and Applications to Biomedical Image Encryption

An innovative model of a fractional order two neuron-based memristive autapses Hopfield Neural Network (HNN) impacted by external electromagnetic radiation is described in this study. Firstly, the system mentioned above is modeled in the fractional-order form. The Adomian decomposition is the foundation of the numerical simulation technique. In terms of the stability requirement of fractional-order systems, the bifurcation tools connected to Lyapunov exponents show the system’s rich dynamical behavior, including a line of equilibrium which are all unstable with regards to the stability condition of fractional-order systems. Investigating the effect of the fractional order (q) on the dynamics of the system is of particular interest. It reveals that, for certain sited periodic regions alone, the system is chaotic throughout the variation of (q). Furthermore, as the several bifurcation diagrams demonstrate, the Memristor Autapse and external electromagnetic radiation have a significant impact on the dynamics of the suggested system. Lastly, a biomedical image encryption approach based on the HNN system is described within the framework of digital cryptography. This scheme offers results with a greater level of security than those achieved by traditional chaos-based communications methods. Image data can be protected in real-world information exchange using this suggested encryption scheme, which is successfully resistant to both statistical and entropy attacks.