Effects of degree distributions on signal propagation in noisy feedforward neural networks

We focus on the effects of degree distributions on signal propagation in noisy feedforward networks (FFNs) based on the FitzHugh-Nagumo neuron model. Three FFN topologies are constructed with the same number of synaptic connections in each layer, but different distributions for both the in-degree and out-degree of neurons as identical, uniform and exponential. It is found that the propagation of firing patterns and firing rates are affected by the degree distributions of neurons in the FFNs. The output firing rates in three FFN topologies without noise is nonlinearly dependent on their input firing rates, and it can be increased steadily by increasing noise intensity. The firing patterns of three FFN topologies can also be influenced by the noise and connection probability. Interestingly, an optimal parameter area corresponding to both the noise intensity and connection probability is found for the propagation of spiking regularity in three FFN topologies respectively. In addition, the firing synchronization of different layers in three topologies differs obviously from one another. Moreover, synfire-enhanced coherence resonance emerges in the later layers of the three FFN topologies. These results suggest that the degree distributions of neurons are a key factor that can modulate both the propagation of the firing rates and firing patterns in FFNs.