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arXiv · 1507.07884

The success of complex networks at criticality

Victor Hernandez-Urbina·Tom L. Underwood·J. Michael Herrmann
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Abstract

In spiking neural networks an action potential could in principle trigger subsequent spikes in the neighbourhood of the initial neuron. A successful spike is that which trigger subsequent spikes giving rise to cascading behaviour within the system. In this study we introduce a metric to assess the success of spikes emitted by integrate-and-fire neurons arranged in complex topologies and whose collective behaviour is undergoing a phase transition that is identified by neuronal avalanches that become clusters of activation whose distribution of sizes can be approximated by a power-law. In numerical simulations we report that scale-free networks with the small-world property is the structure in which neurons possess more successful spikes. As well, we conclude both analytically and in numerical simulations that fully-connected networks are structures in which neurons perform worse. Additionally, we study how the small-world property affects spiking behaviour and its success in scale-free networks.

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Victor Hernandez-Urbina, Tom L. Underwood, J. Michael Herrmann. 2015-07-28. The success of complex networks at criticality. https://arxiv.org/abs/1507.07884

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