Fractional-order heterogeneous memristive Rulkov neuronal network and its medical image watermarking application

This article proposes a novel fractional heterogeneous neural network by coupling a Rulkov neuron with a Hopfield neural network (FRHNN), utilizing memristors for emulating neural synapses. The study firstly demonstrates the coexistence of multiple firing patterns through phase diagrams, Lyapunov exponents (LEs), and bifurcation diagrams. Secondly, the parameter related firing behaviors are described through two-parameter bifurcation diagrams. Subsequently, local attraction basins reveal multi-stability phenomena related to initial values. Moreover, the proposed model is implemented on a microcomputer-based ARM platform, and the experimental results correspond to the numerical simulations. Finally, the article explores the application of digital watermarking for medical images, illustrating its features of excellent imperceptibility, extensive key space, and robustness against attacks including noise and cropping.