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In this article, we construct an excitable memristive diffusive neuron model by considering a biophysical slow–fast bursting oscillator and study the effects of electromagnetic induction on the dynamics of the single model as well as the coupled systems. We explore various firing regimes such as tonic spiking, bursting, and mixed-mode oscillations depending on the bifurcation structure with different injected current stimuli, then perform a comparative analysis on the synchronization of the coupled oscillators by setting the model into two different network architectures. First, a diffusively coupled network is considered, and later a global network is constructed. The results suggest that the diffusively connected neurons show complete synchronization at higher couplings for bursting and tonic spiking regimes. Furthermore, we show that the extended spatial system can generate spiral-like patterns in the vicinity of a Hopf …