Cognitive Neurodynamics

, Volume 13, Issue 1, pp 53–73 | Cite as

Burst synchronization in a scale-free neuronal network with inhibitory spike-timing-dependent plasticity

  • Sang-Yoon Kim
  • Woochang LimEmail author
Original Article


We are concerned about burst synchronization (BS), related to neural information processes in health and disease, in the Barabási–Albert scale-free network (SFN) composed of inhibitory bursting Hindmarsh–Rose neurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without considering iSTDP, BS was found to appear in a range of noise intensities for fixed synaptic inhibition strengths. In contrast, in our present work, we take into consideration iSTDP and investigate its effect on BS by varying the noise intensity. Our new main result is to find occurrence of a Matthew effect in inhibitory synaptic plasticity: good BS gets better via LTD, while bad BS get worse via LTP. This kind of Matthew effect in inhibitory synaptic plasticity is in contrast to that in excitatory synaptic plasticity where good (bad) synchronization gets better (worse) via LTP (LTD). We note that, due to inhibition, the roles of LTD and LTP in inhibitory synaptic plasticity are reversed in comparison with those in excitatory synaptic plasticity. Moreover, emergences of LTD and LTP of synaptic inhibition strengths are intensively investigated via a microscopic method based on the distributions of time delays between the pre- and the post-synaptic burst onset times. Finally, in the presence of iSTDP we investigate the effects of network architecture on BS by varying the symmetric attachment degree \(l^*\) and the asymmetry parameter \(\varDelta l\) in the SFN.


Inhibitory spike-timing-dependent plasticity Burst synchronization Scale-free network Bursting neurons 



This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 20162007688).


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Institute for Computational Neuroscience and Department of Science EducationDaegu National University of EducationDaeguKorea

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