Enhancing weak signal propagation by intra- and inter-layer global couplings in a feedforward network

The brain can efficiently receive and process weak signals, and reproducing signal amplification is an important task. We investigate weak signal propagation in a coupled feedforward network composed of bistable neurons, where the neuron connections include intra-layer and inter-layer couplings. We find that both intra- and inter-layer couplings both determine whether the weak signal propagation is enhanced or attenuated. Both the numerical and analytical results indicate that weak signal enhancement is dependent on two conditions: I. the intra-layer coupling strength is less than the critical value at which neurons in the first layer are fully synchronized; II. the inter-layer coupling strength is greater than the critical value at which neurons in the second layer exhibit a Hopf bifurcation. It has been revealed that the most significant signal enhancement occurs when the intra-layer coupling is less than a critical value and the inter-layer coupling reaches a critical value. Additionally, we have examined the impact of the weak signal frequency on signal propagation. Our qualitative analysis of the Hopf bifurcation provides a theoretical basis for the study of weak signal propagation in multilayer networks.