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In this paper, we study an excitable, biophysical system that supports wave propagation of nerve impulses. We consider a slow–fast, FitzHugh–Rinzel neuron model where only the membrane voltage interacts diffusively, giving rise to the formation of spatiotemporal patterns. We focus on local, nonlinear excitations and diverse neural responses in an excitable one-and two-dimensional configuration of diffusively coupled FitzHugh–Rinzel neurons. The study of the emerging spatiotemporal patterns is essential in understanding the working mechanism in different brain areas. We derive analytically the coefficients of the amplitude equations in the vicinity of Hopf bifurcations and characterize various patterns, including spirals exhibiting complex geometric substructures. Furthermore, we derive analytically the condition for the development of antispirals in the neighborhood of the bifurcation point. The emergence of …