Cognitive Neurodynamics

, Volume 12, Issue 2, pp 225–234 | Cite as

Measuring spike timing distance in the Hindmarsh–Rose neurons

Research Article


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.


Spike timing distance Synchronization Hindmarsh–Rose neuron Common noise 



This research was supported by the National Natural Science Foundation of China (Grant Nos. 11772149, 11472126 and 11232007) and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).


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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China

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