Abstract
Synchronous firing patterns and transitions of Hindmarsh–Rose small-world neuronal network are studied in this work. With the same external stimuli current, it is shown that the synchronous state of the Newman and Watts (NW) small-world neuronal network is completely determined by its external stimuli current, have nothing about the coupling strength \(C\) as well as the connection probability \(p\); a qualitative explanation is proposed for the opposite changes of the minimum critical coupling strength \(C_{\mathrm{mcc}}\) and the minimum connection probability \(p_{\mathrm{mcp}}\). With two different amplitude stimuli current, only almost complete synchronization can be achieved, and the firing patterns of the synchronized NW small-world neuronal network only distributes the interval with two endpoints, which just correspond to the two modes in a single model neuron with these two kinds of amplitude stimuli current.
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