Volume 106, Number 6, June 2014
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||11 June 2014|
Propagation failure of excitation waves on trees and random networks
1 Departament de Física Fonamental, Universitat de Barcelona - Martí i Franquès 1, 08028 Barcelona, Spain
2 Institut für Theoretische Physik, Technische Universität Berlin - Hardenbergstraße 36, 10623 Berlin, Germany
3 Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society - Faradayweg 4-6, 14195 Berlin, Germany
Received: 28 March 2014
Accepted: 22 May 2014
Excitation waves are studied on trees and random networks of coupled active elements. Undamped propagation of such waves is observed in those networks. It represents an excursion from the resting state and a relaxation back to it for each node. However, the degrees of the nodes influence drastically the dynamics. Excitation propagates more slowly through nodes with larger degrees and beyond some critical degree waves lose their stability and disappear. For regular trees with a fixed branching ratio, the critical degree is determined with an approximate analytical theory which also holds locally for the early stage of excitation spreading in random networks.
PACS: 87.18.Sn – Neural networks and synaptic communication / 89.75.Kd – Patterns / 87.19.lq – Neuronal wave propagation
© EPLA, 2014
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