Noise-induced synchronization and regularity in feed-forward-loop motifs

This study explores the impacts of multiple factors (noise, intra-motif coupling, and critical bifurcation parameter) on noise-induced motif synchrony and output regularity in three-node feed-forward-loops (FFLs), distinguishing between coherent FFLs with purely excitatory connections and incoherent FFLs formed by transitioning the intermediate layer to inhibitory connections. Our model utilizes the normal form of Hopf bifurcation (HB), which captures the generic structure of excitability observed in real systems. We find that the addition of noise can optimize motif synchrony and output regularity at the intermediate noise intensities. Our results also suggest that transitioning the excitatory coupling between the intermediate and output layers of the FFL to inhibitory coupling-i.e., moving from the coherent to the incoherent FFL-enhances output regularity but diminishes motif synchrony. This shift towards inhibitory connectivity highlights a trade-off between motif synchrony and output regularity and suggests that the structure of the intermediate layer plays a pivotal role in determining the motif's overall dynamics. Surprisingly, we also discover that both motifs achieve their best output regularity at a moderate level of intra-motif coupling, challenging the common assumption that stronger coupling, especially of the excitatory type, results in improved regularity. Our study provides valuable insights into functional differences in network motifs and offers a direct perspective relevant to the field of complex systems as we consider a normal-form model that pertains to a vast number of individual models experiencing HB.