We consider the Barab\'{a}si-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 iSTDP, burst synchronization (BS ) was found to appear in a range of noise intensities for fixed synaptic inhibition strengths. Here, we investigate the effect of iSTDP on BS by varying the noise intensity. We employ an anti-Hebbian time window for the iSTDP update rule, in contrast to the Hebbian time window for the excitatory STDP. A Matthew effect in inhibitory synaptic plasticity is thus found to occur; good BS (with higher bursting measure) gets better via long-term depression (LTD) , while bad BS (with lower bursting measure) gets worse via long-term potentiation (LTP) . This kind of Matthew effect  is in contrast to that in excitatory synaptic plasticity where good (bad) synchronization gets better (worse) via LTP (LTD). Furthermore, 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 , and Matthew effects in inhibitory synaptic plasticity are also found to occur by varying l^* and \Delta l .
We are concerned about burst synchronization (BS), related to neural information processes in health and disease, in the Barab\'{a}si-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 .
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