Initial-flux dynamics of discrete memristive hopfield neural network with recurrence quantification analysis

Discrete memristive neural systems are of great interest because of their complex dynamics and potential applications in secure information processing. In this study, a discrete memristive Hopfield neural network with a memristive self-feedback pathway is proposed and studied from the perspectives of dynamical analysis, hardware validation, and secure image processing. By introducing a flux-controlled memristor into a two-neuron discrete Hopfield neural network, the fixed-point line and its transverse stability are analyzed. Numerical results reveal that different initial flux states can induce distinct coexisting bifurcation routes, including period-doubling and Neimark–Sacker bifurcations, together with periodic, quasi-periodic, and chaotic behaviors in the parameter space. To further characterize the evolution of these states, recurrence quantification analysis is employed under parameter variation and Gaussian noise perturbation, showing clear differences in recurrence structure and noise sensitivity for different initial conditions. An FPGA-based implementation is then developed to verify the physical realizability of the proposed map, and the measured waveforms are consistent with numerical simulations. Finally, the generated chaotic sequences are applied to RGB image encryption, demonstrating good performance in secure image protection. The results indicate that the proposed model provides a useful framework for both nonlinear dynamical analysis and engineering applications.