Neural Signal Tuned by Random Long-range Connections in Coupled FitzHugh--Nagumo Neurons Systems

We investigate the effect of random long-range connections on signal propagation in an array of coupled FitzHugh--Nagumo (FHN) neurons. The neural network can be obtained by randomly adding a small fraction of shortcuts in an originally locally coupled one-dimensional chain. It is shown that when the first neuron is subjected to external stimuli, it fires and excites its connected neighbours, such that the neural signal may propagate along the chain favoured by the shortcuts. Moreover, there exists an optimal number of shortcuts which can lead to the most synchronous behaviour. In addition, how the region of the fraction of shortcuts varies with the coupling strength is also discussed. These results suggest that topological disorder in the neural network may play a vital role in helping information processing in living systems.