Propagation failure of excitation waves on trees and random networks

Abstract

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.

arXiv comment7 pages, 7 figures, submitted to epl

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• Excitation Waves on a Minimal Small-World Model
• Stationary patterns in star networks of bistable units: Theory and application to chemical reactions
• Propagation of extreme events in multiplex neuronal networks
• Variability of collective dynamics in random tree networks of strongly-coupled stochastic excitable elements