Effect of network architecture on burst and spike synchronization in a scale-free network of bursting neurons

Abstract

We investigate the effect of network architecture on burst and spike synchronization in a directed scale-free network (SFN) of bursting neurons, evolved via two independent α− and β−processes.The α−process corresponds to a directed version of the Barabási-Albert SFN model with growth and preferential attachment, while for the β−process only preferential attachments between preexisting nodes are made without addition of new nodes. We first consider the "pure" α−process of symmetric preferential attachment (with the same in-and out-degrees), and study emergence of burst and spike synchronization by varying the coupling strength J and the noise intensity D for a fixed attachment degree. Characterizations of burst and spike synchronization are also made by employing realistic order parameters and statistical-mechanical measures. Next, we choose appropriate values of J and D where only the burst synchronization occurs, and investigate the effect of the scale-free connectivity on the burst synchronization by varying (1) the symmetric attachment degree and (2) the asymmetry parameter (representing deviation from the symmetric case) in the α−process, and (3) the occurrence probability of the β−process. In all these three cases, changes in the type and the degree of population synchronization are studied in connection with the network topology such as the degree distribution, the average path length L p , and the betweenness centralization B c . It is thus found that not only L p and B c (affecting global communication between nodes) but also the in-degree distribution (affecting individual dynamics) are important network factors for effective population synchronization in SFNs.

Effect of spike-timing-dependent plasticity on stochastic burst synchronization in a scale-free neuronal network

“…Hence, the majority of peripheral nodes have their degrees near the peak at d (in) = 10, while the minority of hubs have their degrees in the long-tail part. Based on the degree distribution (showing a power-law decay), we classify the nodes into the hub group (composed of the head hub with the highest degree and the secondary hubs with higher degrees) and the peripheral group (consisting of a majority of peripheral nodes with lower degrees) in the following way [148,149]. We choose an appropriate threshold d (in) th separating the hub and the peripheral groups in the distribution of in-degrees d (in) in Fig.…”

“…To see emergence of burst synchronization, we employ an (experimentally-obtainable) instantaneous population burst rate (IPBR) which is often used as a collective quantity showing bursting behaviors. This IPBR may be obtained from the raster plot of burst onset times [80,149,150]. To obtain a smooth IPBR, we employ the kernel density estimation (kernel smoother) [151].…”

“…Effects of l * on network topology were characterized in Refs. [148,149], where the group properties of the SFN were studied in terms of the average path length L p and the betweenness centralization B c by varying l * . The average path length L p (representing typical separation between two nodes in the network) is obtained via the average of the shortest path lengths of all nodal pairs (see Eq.…”

Graph Theory and Brain Connectivity in Alzheimer’s Disease

“…The distribution of connections is neither random nor uniform. The connectivity distribution follows a power law dependence (Kim and Lim 2016). This produces a scale free network with hubs.…”

Cluster Burst Synchronization in A Scale-Free Network of Inhibitory Bursting Neurons

“…As clearly shown in Fig. 2 As macroscopic quantities showing the whole-and the sub-population behaviors, we employ the instantaneous whole population burst rate (IWPBR) R w (t) and the instantaneous sub-population burst rate (ISPBR) R (I) s (t) (I=1, 2, 3) which may be obtained from the raster plots in the whole population and in the clusters, respectively [30][31][32][33]. To obtain a smooth IWPBR R w (t), we employ the kernel density estimation (kernel smoother) [103].…”