In the present paper, a simple spike timing distance is defined which can be used to measure the degree of synchronization
with the information only encoded in the precise timing of the spike trains. Via calculating the spike timing distance
defined in this paper, the spike train similarity of uncoupled Hindmarsh–Rose neurons in bursting or spiking states with
different initial conditions is investigated and the results are compared with other spike train distance measures. Later, the
spike timing distance measure is applied to study the synchronization of coupled or common noise-stimulated neurons.
Counterintuitively, the addition of weak coupling or common noise doesn’t enhance the degree of synchronization
although after critical values, both of them can induce complete synchronizations. More interestingly, the common noise
plays opposite roles for weak and strong enough couplings. Finally, it should be noted that the measure defined in this
paper can be extended to measure large neuronal ensembles and the lag synchronization.

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• Measuring spike timing distance in the Hindmarsh–Rose neurons