Non-normal dynamics on nonreciprocal networks: Reactivity and effective dimensionality in neural circuits.

Nonreciprocal interactions are widespread in neural circuits, arising both within local excitatory-inhibitory (E/I) dynamics and through directed coupling between distinct populations. Here we investigate how these two levels of asymmetry combine in a modified Wilson-Cowan model of locally non-normal E/I populations connected by directed excitatory projections. We analyze minimal three-node motifs interpolating between a cyclic feedback architecture and a purely feedforward chain. We find that cyclic coupling is largely reducible to an effective shift of the local excitatory coupling, preserving the activation scaling of an isolated E/I module. Feedforward coupling, by contrast, introduces a structural source of non-normality: It produces stage-dependent activation scaling and enhances transient reactivity even at fixed local non-normality. With intrinsic finite-size noise, both motifs exhibit fluctuation-driven switching between inactive and active states but organize activity differently: Feedback promotes coherent, correlated activation, whereas feedforward coupling generates sequential, steplike propagation. These results show how local and structural nonreciprocity play distinct roles in shaping transient amplification and noise-driven dynamics in coupled neural populations, thereby contributing to the growing understanding of the dynamical effects of non-normality across complex systems.