da Fontoura Costa, Luciano. 2008. "Spiking Oscillations in Complex Neuronal Networks." (Working Paper)

Abstract

"Although integrate-and-fire dynamics possesses special importance because of its intrinsic relationship with neuronal information processing, it has been rarely considered in investigations of the structure-dynamics relationship in complex networks. However, the pronounced non-linearities of this type of dynamics implies a particularly rich variety of attractors and activity patterns, including avalanches of spikes and confinement of activation inside topological communities. Both these remarkable phenomena take place during the transient activation regime. In this work we investigate the oscillations and waves which appear in the equilibrium regime of integrate-and-fire complex neuronal networks. In order to do so, one of the restrictions of the equivalent models reported previously, namely a reasonable uniformity of degrees, is circumvented by subsuming the nodes with identical degree found inside each hierarchical levels into respective equivalent nodes. It has been shown, by considering uniformly-random and small-world theoretical types of networks, that the so-obtained model is capable of predicting the respective integrate-and-fire dynamics with great accuracy regarding both temporal dynamics and power spectrum features. The causes and properties of the stable waves emerging along the equilibrium regime of the complex neuronal networks are identified and discussed. Of particular relevance are the twin correlations defined by the different frequencies of groups of nodes at different concentric levels. The transient and equilibrium regimes are also clearly identifiable from the total activation in the networks, corresponding respectively to conservative and dissipative dynamics."