Random long-range connections induce activity of complex Hindmarsh–Rose neural networks

In this paper, we investigate how activity of complex neural networks depends on random long-range connections. Network elements are described by Hindmarsh–Rose (HR) neurons assumed to be inactive. It is found that for a given coupling strength, when the number of random connections (or randomness) is greater than a threshold, the spiking neurons, which are absent in the nearest-neighbor neural network, occur. The spiking activity becomes stronger in intensity and higher in frequency as the randomness is further increased. These phenomena imply that random long-range connections can induce and enhance the activity of neural networks. Furthermore, the possible mechanism behind the action of random long-range connections is also addressed. Our results may provide a useful hint for understanding the properties of collective dynamics in coupled real neurons.