We consider a directed Barabási-Albert scale-free network model with symmetric preferential attachment with the same in- and out-degrees, and study emergence of sparsely synchronized rhythms for a fixed attachment degree in an inhibitory population of fast spiking Izhikevich interneurons. For a study on the fast sparsely synchronized rhythms, we fix $J$ (synaptic inhibition strength) at a sufficiently large value, and investigate the population states by increasing $D$ (noise intensity). For small $D$, full synchronization with the same population-rhythm frequency $f_p$ and mean firing rate (MFR) $f_i$ of individual neurons occurs, while for sufficiently large $D$ partial synchronization with $f_p > {\langle f_i \rangle}$ ($\langle f_i \rangle$: ensemble-averaged MFR) appears due to intermittent discharge of individual neurons; particularly, the case of $f_p > 4 {\langle f_i \rangle}$ is referred to as sparse synchronization. Only for the partial and sparse synchronization, MFRs and contributions of individual neuronal dynamics to population synchronization change depending on their degrees, unlike the case of full synchronization. Consequently, dynamics of individual neurons reveal the inhomogeneous network structure for the case of partial and sparse synchronization, which is in contrast to the case of statistically homogeneous random graphs and small-world networks. Finally, we investigate the effect of network architecture on sparse synchronization in the following three cases: (1) variation in the degree of symmetric attachment (2) asymmetric preferential attachment of new nodes with different in- and out-degrees (3) preferential attachment between pre-existing nodes (without addition of new nodes). In these three cases, both relation between network topology and sparse synchronization and contributions of individual dynamics to the sparse synchronization are discussed.
Effects of T-type and L-type calcium currents on synchronized activity patterns in a model subthalamo-pallidal network
North Carolina A&T State University（北卡罗来纳农业州立大学）；Indiana University Indianapolis（印第安纳大学印第安纳波利斯分校）；Stark Neurosciences Research Institute, Indiana University School of Medicine（斯塔克神经科学研究所，印第安纳大学医学院）；Department of Mathematics, East Carolina University（东卡罗来纳大学数学系）；Alliance for Brain Stimulation, College of Allied Health Sciences, East Carolina University（脑刺激联盟，东卡罗来纳大学健康科学学院）
Intrinsic Resonance depends on Network Size of Coupled-Delayed Interacting Oscillators
Universidad Católica del Maule（天主教马乌莱大学）；Universidad Técnica Federico Santa María（费德里科·圣玛丽亚技术大学）；Ikerbasque: The Basque Foundation for Science（伊卡巴斯克：巴斯克科学基金会）；Bio-Bizkaia Health Research Institute（生物比斯开健康研究所）；University of the Basque Country（巴斯克大学）；Brain Dynamics Lab, Interdisciplinary Center of Biomedical and Engineering Research for Health, Universidad de Valparaíso（瓦尔帕莱索大学生物医学与健康工程研究跨学科中心脑动力学实验室）
