Trapping of phase fronts and twisted spirals in periodically forced oscillatory media

Abstract

The control of pattern formation is an important problem in engineering of spatially extended self-organized systems. A wide class of systems showing spontaneously formed waves and patterns can be summarized under the generic term "oscillatory media". They may be considered as a composition of a large number of coupled subsystems. The dynamics of each subsystem is oscillatory. Complex phenomena like the formation of patterns and waves or spatio-temporal chaos comes through the interaction between the subsystems. Despite such complex collective behavior the dynamics is very sensitive to feedback or to periodic forcing with frequencies close to an integer ratio of the oscillation frequency of the subsystems.A well-known example is the Belouzov-Zhabotinsky-Reaction, involving the oxidation of an organic compound by bromate in acidic solution. It is a robust oscillatory reaction with striking color changes. Spatiotemporal wave behavior is exhibited in unstirred reaction mixtures [1,2]. For this reaction, application of global periodic forcing was shown to produce various cluster patterns [3,4,5] and induce turbulent regimes [6].Another example which has been extensively studied is the catalytic CO oxidation on Pt(110). The interplay between desorption and surface diffusion of CO, reaction between the two adsorbed species, and an adsobate-driven structural change of the platinum surface can lead to oscillations of the CO and oxygen coverage [7]. In experiments where bulk oscillations were unstable and spatiotemporal chaos spontaneously developed, application of periodic forcing allowed to suppress chemical turbulence, produce intermittent regimes with cascades of amplitude defects, and generate oscillating cellular and labyrinthine patterns [8,9]. Recently, front explosions have been predicted under periodic forcing [10].

Experimental and Theoretical Study of Forced Synchronization of Self-Oscillations in Liquid Ferrocolloid Membranes

“…The structures obtained experimentally in a cell with a ferrocolloid under the action of an external periodic force are similar to those described in [24], where the same structures were observed by the authors in a quasi-twodimensional reaction-diffusion system with a light-sensitive Belousov-Zhabotinsky reaction. This result is convincing evidence that the phenomenon of synchronization when pairing the internal oscillatory dynamics with an external periodic action can arise in a variety of chemical, biological, and other systems [41][42][43][44][45][46]. 4.…”