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In this paper, we study spiking synchronization in three different types of Hodgkin—Huxley neuronal networks, which are the small-world, regular, and random neuronal networks. All the neurons are subjected to subthreshold stimulus and external noise. It is found that in each of all the neuronal networks there is an optimal strength of noise to induce the maximal spiking synchronization. We further demonstrate that in each of the neuronal networks there is a range of synaptic conductance to induce the effect that an optimal strength of noise maximizes the spiking synchronization. Only when the magnitude of the synaptic conductance is moderate, will the effect be considerable. However, if the synaptic conductance is small or large, the effect vanishes. As the connections between neurons increase, the synaptic conductance to maximize the effect decreases. Therefore, we show quantitatively that the noise-induced maximal synchronization in the Hodgkin—Huxley neuronal network is a general effect, regardless of the specific type of neuronal network.

Because a brain consists of tremendous neuronal networks with different neuron numbers ranging from tens to tens of thousands, we study the coherence resonance due to ion channel noises in globally coupled neuronal networks with different neuron numbers. We confirm that for all neuronal networks with different neuron numbers there exist the array enhanced coherence resonance and the optimal synaptic conductance to cause the maximal spiking coherence. Furthermoremore, the enhancement effects of coupling on spiking coherence and on optimal synaptic conductance are almost the same, regardless of the neuron numbers in the neuronal networks. Therefore for all the neuronal networks with different neuron numbers in the brain, relative weak synaptic conductance (0.1 mS/cm2) is sufficient to induce the maximal spiking coherence and the best sub-threshold signal encoding.