<p>Bridging the gap between computational efficiency and biophysical fidelity remains a central challenge in developing next-generation neuromorphic systems. Although traditional discrete chaotic neuron models are computationally efficient, they often neglect the nonlinear influence of electromagnetic radiation (EMR). Accordingly, this work develops a discrete memristive improved chaotic neuron (DMICN) model by integrating a discrete threshold memristor to characterize the nonlinear feedback of EMR on membrane potential. The proposed framework replaces the traditional Sigmoid activation with a hyperbolic tangent function, thereby improving hardware implementation efficiency. Extensive dynamical analysis reveals a diverse repertoire of firing behaviors and identifies transitions between periodic, quasi-periodic, chaotic, and hyperchaotic firing patterns. Notably, the DMICN model exhibits a unique initial-offset boosting behavior, and the periodic symmetry of the memconductance induces infinite coexisting attractors that are equidistantly distributed in the phase plane. The engineering feasibility of the DMICN model is validated through PSIM-based analog simulations and FPGA-based digital implementation. Moreover, a pseudo-random number generator is developed from its chaotic and hyperchaotic state sequences, and the generated bitstreams pass NIST SP800-22 tests. These results highlight the potential of the proposed model for neuromorphic computing applications.</p>