Oscillatory cluster patterns in a homogeneous chemical system with global feedback

Abstract

Oscillatory clusters are sets of domains in which nearly all elements in a given domain oscillate with the same amplitude and phase. They play an important role in understanding coupled neuron systems. In the simplest case, a system consists of two clusters that oscillate in antiphase and can each occupy multiple fixed spatial domains. Examples of cluster behaviour in extended chemical systems are rare, but have been shown to resemble standing waves, except that they lack a characteristic wavelength. Here we report the observation of so-called 'localized clusters'--periodic antiphase oscillations in one part of the medium, while the remainder appears uniform--in the Belousov-Zhabotinsky reaction-diffusion system with photochemical global feedback. We also observe standing clusters with fixed spatial domains that oscillate periodically in time and occupy the entire medium, and irregular clusters with no periodicity in either space or time, with standing clusters transforming into irregular clusters and then into localized clusters as the strength of the global negative feedback is gradually increased. By incorporating the effects of global feedback into a model of the reaction, we are able to simulate successfully the experimental data.

Propagating Spiral Waves Obtained in a Catalyst-Immobilized Gel Membrane by the Belousov-Zhabotinsky Reaction System

“…For example, Vanag et al recently showed multi-phase oscillatory cluster pattern formation in a light-driven BZ medium. 40,41 Showalter and his group employed spatiotemporal random, forcing to manifest the constructive role of noise in sub-excitable BZ media. 42,43 They reported the presence of spatiotemporal stochastic resonance in a noisy BZ medium, in which the presence of random variation in external light intensity significantly improved the propagation of wave segments.…”

“…Due to the easy implementation of external perturbation, photosensitive reaction-diffusion media have been employed frequently in an effort to understand the interactions between intrinsic dynamics and external perturbations. [38][39][40][41][42][43][44][45] Among these studies, the photosensitive BZ reaction has been primarily employed as the model system, resulting in the oxidation and bromination of malonic acid by acidic bromate present in a metal catalyst, Ru(bpy)3…”

Temperature control of pattern formation in the Ru(bpy)32+-catalyzed BZ-AOT system

“…The dynamical behaviour of the BZ-AOT system in a continuously stirred batch reactor was followed optically at a wavelength of 600 nm (the absorption maximum of the oxidised form of the catalyst) using a home-made spectrophotometric setup. 30 The wavelength of the stationary patterns was determined from the maximum of their 2D fast Fourier transform (FFT). while some oscillate slightly out-of-phase.…”

Spatial Symmetry Breaking in the Belousov-Zhabotinsky Reaction with Light-Induced Remote Communication

“…Entrainment of spiral wave meandering [5] and the formation of labyrinthine patterns [6] have been found with periodic forcing. Resonance attractors [7] and oscillatory cluster patterns [8] were recently reported in photosensitive BZ systems with different types of global feedback.We study the photosensitive BZ reaction with nonlocal coupling over a wide range of length scales, from much larger than the characteristic reaction-diffusion length scale to length scales that are comparable. The kernel of the feedback alternates from positive (activatory) for short distances to negative (inhibitory) for larger distances.…”