Unidirectional links prefer local firing propagation in the neural network of C. elegans

Understanding the mechanisms of brain functions is currently a hot topic but most studies have been focused on the aspects of synchronization and various partial synchronization. We here study this problem from a new angle of signal propagation, where the local (global) propagation may be related to the status of health (mental disorder). We make a case study on the neural network of C. elegans by presenting a framework where one node is chosen as the source node to generate signals and all the other nodes are chosen as the target nodes. We interestingly find that the existence of the unidirectional links is the key element to generate the local firing propagation and the configuration of the unidirectional links will seriously influence the range of firing propagation. In details, our findings include: (i) The unidirectional links prefer the local firing propagation, while the bidirectional links prefer the global firing propagation. (ii) Multiple source nodes will enhance the firing propagation, where the range of firing propagation for choosing the multiple source nodes from different communities is slightly larger than that from the same community. And (iii) a resonance effect of the range of firing propagation on coupling strength is observed, i.e. there is an optimal coupling strength. Moreover, a brief theoretical analysis is provided to explain these results.