This paper investigates the neuroelectromagnetic behavior of the memristive Rulkov (MR) neuron model and introduces an efficient approximated MR (AMR) formulation constructed using a power-of-2 mapping and a sign-based interaction. Comprehensive dynamic, network-level, and error analyses demonstrate that the AMR model preserves the essential nonlinear properties of the original MR system, including bifurcation structures, Lyapunov spectra, spiking–bursting transitions, and magnetic-flux-induced modulation. Quantitative evaluation shows that the AMR model reproduces MR activity with high accuracy, achieving NRMSE below 2.85% in both spiking and bursting regimes. Network tests on 1000-neuron random graphs and 2-D lattice arrays confirm that the AMR model maintains nearly identical wave-propagation patterns and speeds relative to the MR dynamics. FPGA synthesis results highlight the numerical superiority of the AMR model over all three MR implementations (LUT-based, hybrid, and CORDIC). Specifically, the AMR design provides 88.2% overall saving, increases the maximum operating frequency by up to 138.7%, lowers power consumption by up to 16%, and supports up to 700% more neurons per device. These results confirm that the AMR model offers a compact, high-speed, and hardware-efficient neuromorphic solution while preserving the rich dynamical repertoire of the MR neuron.
