Coupled and forced patterns in reaction–diffusion systems

Abstract

Several reaction-diffusion systems that exhibit temporal periodicity when well mixed also display spatio-temporal pattern formation in a spatially distributed, unstirred configuration. These patterns can be travelling (e.g. spirals, concentric circles, plane waves) or stationary in space (Turing structures, standing waves). The behaviour of coupled and forced temporal oscillators has been well studied, but much less is known about the phenomenology of forced and coupled patterns. We present experimental results focusing primarily on coupled patterns in two chemical systems, the chlorine dioxide-iodine-malonic acid reaction and the Belousov-Zhabotinsky reaction. The observed behaviour can be simulated with simple chemically plausible models.

Optimizing mutual synchronization of rhythmic spatiotemporal patterns in reaction-diffusion systems

“…which yields the largest possible stability of the in-phase synchronized state for general nonlinear interaction of Eq. (27). Thus, H(r, ψ) ∝ −∂Z(r, ψ)/∂ψ is the optimal interaction function in the nonlinear case.…”

“…Among them, rhythmic spatiotemporal patterns, such as oscillating spots, target waves, and rotating spirals, can be regarded as stable limit-cycle oscillations of the reaction-diffusion systems. Synchronization between rhythmic spatiotemporal patterns has been experimentally realized using coupled electrochemical systems exhibiting reaction waves of H 2 O 2 reduction on Pt ring electrodes, where two waves are coupled via the common chemical solution [11], and coupled photosensitive Belousov-Zhabotinsky systems exhibiting spiral patterns, where the two patterns are coupled via video cameras and projectors [12] (see also [19,[26][27][28][29][30]). Synchronization of rhythmic fluid flows has also been studied and its possible importance in global climate has been argued [14,15].…”

Spatiotemporal chaos and quasipatterns in coupled reaction–diffusion systems

“…Coupled systems can produce a variety of states including simple Turing patterns, standing waves, mixes of Turing patterns and spiral waves, square and hexagonal superlattice patterns, and many more [10,11]. Coupled systems are important in biology, especially in neural, ecological and developmental contexts; see [12] for examples and for an overview of selected results.…”

Instabilities and patterns in coupled reaction-diffusion layers

“…These coupled systems are common in the biological world, seen in neural, developmental, and ecological contexts [3]. One example from neuroscience is a neural-glial network, consisting of a layer of neurons connected diffusively to a layer of glial cells, where each layer exhibits dynamics at different time scales.…”

“…For a broad overview of experimental and numerical results for some multilayer systems, see Ref. [3].…”