The development of artificial neural networks requires breaking through the limitations of traditional models to establish architectures that more closely resemble the real characteristics of biological neural systems. This paper proposes a novel locally active discrete memristor model and incorporates it into a Hopfield neural network to investigate the influence of electromagnetic radiation (EMR) on neuronal dynamics. By employing nonlinear analysis methods, the complex dynamical characteristics of the system are systematically examined, including bifurcation diagrams, Lyapunov exponent spectra, phase trajectories, and firing patterns. The results demonstrate that the system exhibits diverse nonlinear behaviors, including multistability, state transitions, and attractor offset control, under different parameter conditions. Moreover, by adjusting the memristor parameter, flexible regulation of the dynamical states can be achieved. To further validate the feasibility of the proposed model, a digital signal processing-based hardware implementation is designed and tested. The findings not only simulate the intricate dynamical responses of neurons under EMR exposure but also reveal rich nonlinear phenomena, providing potential applications in medical diagnosis and secure image encryption.