Interaction order controls stochastic-resonance enhancement and redistribution in delayed multiplex neural networks

Abstract

We investigate stochastic resonance in a hierarchy of delayed excitable systems, from a single FitzHugh--Nagumo neuron to single-layer and duplex networks with autaptic, pairwise, triadic higher-order, and interlayer interactions. The response to weak periodic forcing is characterized by the spectral amplitude at the driving frequency, restricting the stochastic-resonance analysis to deterministically subthreshold regimes. We show that the order and organization of interactions generate distinct resonance regimes. Among the autapse-free single-layer architectures, pairwise coupling produces the largest attainable response, whereas weak triadic coupling minimizes the noise amplitude required for resonance. Delayed autaptic feedback primarily shifts the optimal noise level and, within the configurations investigated, yields a genuine enhancement only when pairwise and triadic interactions coexist, revealing a non-additive coupling effect. In duplex networks, interlayer coupling acts predominantly as a response-equalization mechanism: it enhances the weaker layer, generally at the expense of the stronger one, with the redistribution controlled mainly by the uncoupled resonance-capacity gap. Increasing the interlayer delay generally suppresses this collective response. These results identify interaction order, resonance mismatch, and delay as key control parameters for noise-assisted signal processing in multilayer excitable systems.