Synchronization of bursting Hodgkin-Huxley-type neurons in clustered networks

Abstract

We considered a clustered network of bursting neurons described by the Huber-Braun model. In the upper level of the network we used the connectivity matrix of the cat cerebral cortex network, and in the lower level each cortex area (or cluster) is modelled as a small-world network. There are two different coupling strengths related to inter- and intracluster dynamics. Each bursting cycle is composed of a quiescent period followed by a rapid chaotic sequence of spikes, and we defined a geometric phase which enables us to investigate the onset of synchronized bursting, as the state in which the neuron start bursting at the same time, whereas their spikes may remain uncorrelated. The bursting synchronization of a clustered network has been investigated using an order parameter and the average field of the network in order to identify regimes in which each cluster may display synchronized behavior, whereas the overall network does not. We introduce quantifiers to evaluate the relative contribution of each cluster in the partial synchronized behavior of the whole network. Our main finding is that we typically observe in the clustered network not a complete phase synchronized regime but instead a complex pattern of partial phase synchronization in which different cortical areas may be internally synchronized at distinct phase values, hence they are not externally synchronized, unless the coupling strengths are too large.

Investigation of Details in the Transition to Synchronization in Complex Networks by Using Recurrence Analysis

“…Regarding complex networks, it is known that this kind of system can show emergent behavior, where the global behavior observed is richer than the sum of the individual element behaviors. In this way, the existence of non-monotonic transitions to synchronization as a function of coupling strength in neural networks [26][27][28][29][30], where non-stationary states can be noticed, has been reported in the literature. In some cases, in the transition region, on-off intermittency in the two states has been observed, where the network displays the existence of two locally stable states but globally unstable ones [18,26], as defined in [31].…”

Dynamics of signal propagation and collision in axons

“…The equations are based on experimental measurements on the giant axon of the squid performed at a time when the technique for measuring membrane voltage dependent permeability was still in the works. The model has been extended and applied to numerous studies [22][23][24][25][26][27], has stimulated an enormous amount of research, and has also been extremely influential in advancing the field of neuronal science [28,29]. The equations describe the neuron's membrane as a capacitor in parallel with variable resistors (ionic channels more conveniently modeled as conductances) and Nernst potentials represented by batteries.…”

Phase synchronization of coupled bursting neurons and the generalized Kuramoto model

“…A model of thermally sensitive neurons exhibiting bursting has been proposed by Huber and Braun [43][44][45], which describes spike train patterns experimentally observed in facial cold receptors and hypothalamic neurons of the rat [46], electro-receptors organs of freshwater catfish [47], and caudal photo-receptor of the crayfish [48]. However, the Huber-Braun model has 5 differential equations for each neuron, and computational limitations impose restrictions to its use for large networks [81].…”