Spatiotemporal Networks in Addressable Excitable Media

Abstract

Spatiotemporal networks are studied in a photosensitive Belousov-Zhabotinsky medium that allows both local and nonlocal transmission of excitation. Local transmission occurs via propagating excitation waves, while nonlocal transmission takes place by nondiffusive jumps to destination sites linked to excited sites in the medium. Static, dynamic, and domain link networks are experimentally and computationally characterized. Transitions to synchronized behavior are exhibited with increasing link density, and power-law relations are observed for first-coverage time as a function of link probability.

Spatiotemporal dynamics of networks of excitable nodes

“…We focus on an experimentally realizable network based on the photosensitive Belousov-Zhabotinsky system, 15,16 in which the local excitability can be manipulated via light intensity. 17 We first examine the spread of excitation across the network following a perturbation of the quiescent steady state. The conditions for sustained oscillations or the collapse of the dynamics to the steady state are then characterized.…”

Synchronization of Oscillating Reactions in an Extended Fluid System

“…To our knowledge, there has been only one experimental study of synchronization in a continuous fluid system [18]; however, that study deals with a stagnant fluid system with no mixing. Recent theoretical studies have shown that chaotic fluid mixing can synchronize systems whose size is comparable to the characteristic flow length scale [9][10][11][12][13].…”

Sustained dynamics of a weakly excitable system with nonlocal interactions

“…Network connections of nonoscillatory elements, for instance, give rise to such dynamics and have been studied in various contexts, including gene networks [1], epidemic spreading dynamics [2][3][4][5], and generic excitable units [6][7][8][9][10], Excitable units undergo oscillations in many ways: Simple two excitable systems can exhibit sustained dynamics when delay-coupled [11]; spatially extended excitable media can produce sustained spiral waves by introducing a perturbation leading to the formation of a spiral core [12]; one can even consider interactions at a distance through nonlocal links embedded in spatially extended systems [13][14][15][16], which eventually forms network structures composed of wave propagation and nonlocal interactions.…”