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.

Emergent stochastic oscillations and signal detection in tree networks of excitable elements

“…In order to derive approximations for the scaling of the effective current I ext and the noise intensity D eff , we extend the approach of Kouvaris et al 38 , who considered the propagation of excitable waves in a tree network of identical Fitz-Hugh Nagumo nodes in the absence of noisy inputs. Following their approach, we consider the dynamics of the average membrane potential V g (termed density by Kouvaris et al) in each shell in a tree.…”

Self‐Organized Stationary Patterns in Networks of Bistable Chemical Reactions

“…The interplays between local reaction kinetics (nodes), the physical processes that create coupling (link), and the architecture of the network in such systems can lead to a wealth of self-organized phenomena, including synchronization, [4,6,8] stationary Turing and oscillatory patterns, [9,10,11,12,13] or excitation waves. [14,15,16] Stationary patterns generated via the Turing[17] mechanism have been observed in experiments for both continuous [18] and networked [19] systems. Here, an alternative mechanism for emergence of stationary patterns in networks is experimentally explored.…”

Variability of collective dynamics in random tree networks of strongly coupled stochastic excitable elements

“…In the strong coupling limit, the nodal dynamics is synchronized and nodes within the same generation become statistically indistinguishable. To make use of this fact, we follow the approach presented by Kouvaris et al [43] and extend it to stochastic excitable elements on random tree networks. To this end, we consider the dynamics of the generation-averaged membrane potentials V g := 1 D g j ∈ gen.g V j , g = 0, 1, 2, .…”