In the cerebral cortex, the distribution of excitatory post-synaptic potential exhibits log-normal distribution. Recently, it has been reported that this distribution generates a spontaneous activity. Moreover, this distribution may have useful effect in enhancing abilities of associative memory recall and can induce burst spiking to play a crucial role in memory consolidation. The weak synaptic networks in this log-normal distribution exhibit random network characteristics, while the strong synaptic networks have small-world characteristics. The concern with the functionality of fluctuation of neural activity and duality of synaptic connectivity has been brought to public attention. Therefore, in this study, to determine the relationship between the complexity of spontaneous activity and duality of synaptic connectivity, we introduced a spiking neural network with the duality of synaptic connectivity. Subsequently, we conducted multiscale entropy analysis for spontaneous activity and clustering analysis of emergent spiking pattern. The results revealed that in case wherein strong synaptic connections exhibit intermediate characteristic of small world network, specific spiking patterns arise among the spatio-temporal irregular spiking activity. Additionally, multi-scale entropy profile of the spiking activity exhibits a unimodal maximum peak at a slow temporal scale corresponding to the profile of the actual brain activity.