Analysis of Piecewise-Linear Hopfield Neural Network Model Based on a Novel Fractional-Order Memristor and Its Application to Image Encryption

This paper introduces a novel three-neuron memristive synaptic coupling Piecewise-Linear Hopfield Neural Network (PWL-HNN) and extends it to fractional order. This study delves into studying the dynamical behaviors of the fractional-order memristive PWL-HNN using bifurcation diagrams, largest Lyapunov exponential spectra, Poincare cross-sections, attraction basins, and two-parameter bifurcation diagram, and exploring variations in PWL activation function parameters, memristive coupling strengths, and initial conditions. Subsequently, an equivalent circuit model of the fractional-order memristive PWL-HNN on the Cadence/PSpice platform is developed, verifying its dynamic behavior through circuit simulation experiments. Additionally, a digital circuit of the fractional-order memristive HNN model is implemented on the LabVIEW platform, with NI PXIe equipment utilized for hardware circuit realization. The experimental results align closely with numerical and circuit simulation results, affirming the theoretical analysis's accuracy. Lastly, this paper investigates the generation of a pseudo-random sequence using fractional-order memristive HNN and explores an image encryption algorithm in conjunction with the DNA algorithm, assessing the encryption algorithm's reliability through security analysis.