Title: Burst Synchronization in A Scale-Free Neuronal Network with Inhibitory Spike-Timing-Dependent Plasticity,
Abstract: 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 $\Delta l$ in the SFN.