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No Access Submitted: 21 April 2018 Accepted: 02 August 2018 Published Online: 09 October 2018

Fast regular firings induced by intra- and inter-time delays in two clustered neuronal networks

Chaos 28, 106310 (2018); https://doi.org/10.1063/1.5037142
Xiaojuan Sun1,a), Matjaž Perc2,3,4,b), Jürgen Kurths5,6,c), and Qishao Lu7,d)
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ABSTRACT
In this paper, we consider two clustered neuronal networks with dense intra-synaptic links within each cluster and sparse inter-synaptic links between them. We focus on the effects of intra- and inter-time delays on the spiking regularity and timing in both clusters. With the aid of simulation results, we show that intermediate intra- and inter-time delays are able to separately induce fast regular firing −spiking activity with a high firing rate as well as a high spiking regularity. Moreover, when both intra- and inter-time delays are present, we find that fast regular firings are induced much more frequently than if only a single type of delay is present in the system. Our results indicate that appropriately adjusted intra- and inter-time delays can significantly facilitate fast regular firing in neuronal networks. Based on a detailed analysis, we conjecture that this is most likely when the largest value of common divisors of the intra- and inter-time delays falls into a range where fast regular firings are induced by suitable intra- or inter-time delays alone.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (NNSFC) (Grant No. 11472061). Matjaž Perc acknowledges support from the Slovenian Research Agency (Grant Nos. P5-0027 and J1-7009). Jürgen Kurths acknowledges support by the DFG/FAPESP (Project No. IRTG 1740/TRP 2011/50151-0).

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