<p>In this paper, a new memristive Chialvo neuron map is proposed by incorporating a locally active discrete memristor into the original Chialvo neuron model. The introduced memristor exhibits local activity, nonvolatility, and bistability, which fundamentally enrich the neuron dynamics. Equilibrium points and their stability are analyzed as functions of the memristive coupling strength, revealing that the number of equilibrium points increases with increasing memristor strength, indicating enhanced multistability. Comprehensive dynamical analyses based on bifurcation diagrams and largest Lyapunov exponents demonstrate that the proposed model exhibits a wide range of firing behaviors, including periodic, quasiperiodic, and chaotic dynamics. It is shown that increasing the memristive coupling strength generally suppresses chaotic regions, a result further confirmed by spectral entropy analysis. Time-series and phase-space investigations reveal that the memristor can induce qualitative transitions between different firing patterns and modify oscillation periods. In contrast to the original Chialvo model, which mainly exhibits bistability between resting and oscillatory states, the proposed memristive model is capable of exhibiting bistability and multistability between distinct oscillatory attractors, strongly dependent on the initial state of the memristor. Furthermore, the effect of stochastic perturbations is examined, showing that additive noise can induce spiking and bursting dynamics in parameter regions where the noise-free system remains quiescent. As the memristive coupling strength increases, a lower noise intensity is required to induce oscillatory activity.</p>