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Front Comput Neurosci. 2012 Aug 6;6:50. doi: 10.3389/fncom.2012.00050. eCollection 2012.

Building blocks of self-sustained activity in a simple deterministic model of excitable neural networks.

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1
School of Engineering and Science, Jacobs University Bremen Bremen, Germany.

Abstract

Understanding the interplay of topology and dynamics of excitable neural networks is one of the major challenges in computational neuroscience. Here we employ a simple deterministic excitable model to explore how network-wide activation patterns are shaped by network architecture. Our observables are co-activation patterns, together with the average activity of the network and the periodicities in the excitation density. Our main results are: (1) the dependence of the correlation between the adjacency matrix and the instantaneous (zero time delay) co-activation matrix on global network features (clustering, modularity, scale-free degree distribution), (2) a correlation between the average activity and the amount of small cycles in the graph, and (3) a microscopic understanding of the contributions by 3-node and 4-node cycles to sustained activity.

KEYWORDS:

cellular automaton; cycles; excitable dynamics; self-sustained activity

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