Breathing Spots in a Reaction-Diffusion System

Abstract

A quasi-2-dimensional stationary spot in a disk-shaped chemical reactor is observed to bifurcate to an oscillating spot when a control parameter is increased beyond a critical value. Further increase of the control parameter leads to the collapse and disappearance of the spot. Analysis of a bistable activator-inhibitor model indicates that the observed behavior is a consequence of interaction of the front with the boundary near a parity breaking front bifurcation.PACS numbers: 47.54.+r, 82.20.Mj, 82.40.Ck Oscillations in spatially extended chemical systems are often the result of underlying oscillating dynamics of the local chemical kinetics [1]. In systems with nonuniform spatial structures, oscillations may also be driven by diffusion. Spiral waves and breathing spots in excitable and bistable media are examples of oscillatory behaviors where the local kinetics without diffusion converge to stationary uniform states, while spatial structures undergo oscillations. Chemical spirals have been observed and studied for more than two decades [2], but breathing spots have not been previously observed although they have been found in numerical and analytical studies of activator-inhibitor models [3,4]. Figure 1 shows an example of the breathing spots observed in our study of a ferrocyanide-iodate-sulfite (FIS) reaction [5] in a quasi-2-dimensional reactor. The breathing motion arises as a control parameter is increased and an initially stable circular front (the spot boundary) becomes unstable. Further increase in control parameter eventually leads to the front rebounding from the cell boundary and propagating inward until the spot collapses and disappears. The breathing motion is interpreted as transitions between left and right propagating fronts near a parity breaking front bifurcation [6]. The rebound phenomenon leading to spot collapse is attributed to crossing the front bifurcation as the control parameter is increased. We will first describe the experimental system and then present the observations and the interpretation of the results in terms of a model reaction-diffusion system.The chemical patterns form in a thin gel layer that allows reaction and diffusion processes but prevents convection. The apparatus is similar to that used by Lee et al. [7]. A polyacrylamide gel layer (25 mm diameter, 0.3 mm thick) is in contact with a well-stirred reservoir (2.8 ml volume) that is continuously fed with reagents of the FIS reaction. Reagents are fed first to a premixer (1.0 ml volume) in two streams, one with H 2 SO 4 and NaIO and the other with Na 2 SO 3 and K 4 Fe(CN) 6 · 3H 2 O. The output of the premixer is fed to a stirred reservoir that is in contact with the gel layer. The reservoir diameter is 22 mm; thus the outer 1.5 mm width edge of the gel is not in contact with the reservoir. The entire system is immersed in a water bath maintained at T = 30• C. The side of the gel opposite to the chemical reservoir is a window through which the gel is illuminated with blue light (400-440 nm), and the patterns are vie...

Scenarios of domain pattern formation in a reaction-diffusion system

“…This instability leads to the transformation of the static spot into a radially-symmetric pulsating (breathing) spot. Such pulsating spots were observed in the numerical simulations and the experiments [10][11][12]36,37]. The instability occurs when the radius of a spot R The results of the analysis of the instabilities of simple shapes (spots and stripes) and the results of the numerical simulations can be presented on the diagram (Fig.…”

Order parameter equations for front transitions: Planar and circular fronts

“…[42], which studies the effect of boundaries on spot dynamics, reports on the observation of stationary, breathing, and rebounding spots. Interaction between fronts may similarly lead to stationary, oscillating, and collapsing domains [10][11][12][13][14][15][16][17][18].…”

Interaction of Ising-Bloch fronts with Dirichlet boundaries

“…[10,11,12,13,21] in the context of this bifurcation. It has been widely used to model patterns in reactions like the Belousov-Zhabotinsky (BZ) reaction [22,23,24,25,26], Ferrocyanide-Iodate-Sulfite (FIS) reaction [4] and Chlorite-Iodide-Malonic-Acid reaction(CIMA) [14,15,16]. The two component reaction-diffusion system, with v(x, t) impeding the production of u(x, t), is given by…”

“…In spatially extended reaction-diffusion systems far from equilibrium, the interplay of the diffusion and reaction processes is frequently associated with the formation of spatial or temporal patterns in the concentration fields [1,2,3,4,5,6]. One such example is a front-like structure connecting two different homogeneous steady states.…”

“…An adiabatic description of nonuniform front motion along the lines of [4] is inadequate. It relies on nullclines and fails to explain the jumps from one nullcline to another or the influence of fixed points.…”