Synchronization in the discrete chemical oscillation system

Abstract

The properties of the coupling between chemical oscillators were studied in the discrete chemical oscillation system which was realized by immersing cation exchange beads loaded with ferroin in the Belousov–Zabotinskii reaction solution. A phase diagram of coupling states was obtained as a function of natural frequencies of oscillators and the distance d between oscillators. The synchronization was found not to be attributed to a simple entrainment of the slower oscillator by the faster one. Various entrainments between oscillators occurred depending on ratios of natural frequencies in the uncoupled state. A chaotic behavior was found at the boundary between stably coupled regions with frequency ratios of n/1 where n is an integer. Furthermore, effects of external perturbation on the coupling were investigated. Irregular oscillations were induced by illumination with a He–Ne laser light, which strongly depended on the phase of oscillator at the beginning of illumination. Such irregular behaviors were localized within the illuminated bead. This indicates that two oscillators are decoupled by illumination.

Responses of an immobilized-catalyst Belousov–Zabotinsky reaction system to electric fields

“…19,20 The former corresponds to a forced entrainment, where the electric field changes the concentration of Br Ϫ ions around beads by an electrostatic effect and consequently controls the redox reaction on beads. On the other hand, entrainment in the coupled oscillator system corresponds to a mutual one, where entrainment occurs through the diffusion of the activator HBrO 2 .…”

“…Experimental procedures have been described in detail in an earlier paper 19 and are briefly mentioned. Water was distilled twice from deionized water and filtered through a 0.1 m membrane filter.…”

“…Very recently, we have utilized such beads as chemical oscillators and investigated properties of coupling between two oscillators. 19,20 In respect of both coupling behaviors and the spatial size of the oscillator, this oscillator seems to have the potential of serving as a model for biological oscillators. There is now a great interest in subjecting this type of oscillator to external electric fields.…”

Insights into collective cell behaviour from populations of coupled chemical oscillators

“…Since the concentrations of HBrO 2 and Br -decay in the surrounding solution (through disproportionation and process A), the strength of the coupling is determined by the distance between the beads and the size of the beads relative to the reaction timescale. 20,21 Using a spatial light modulator (SLM), the light intensity projected on a bead can be varied dynamically according to an algorithm ( Figure 2b). 27 If the transmitted light intensity of a particular bead increases, then the intensity of light projected onto a different bead can also be increased, initiating production of HBrO 2 .…”

Competition between global feedback and diffusion in coupled Belousov-Zhabotinsky oscillators

“…This can be considered to be the simplest oscillatory cluster pattern. One can imagine that in-phase oscillation is observed with diffusive coupling only and no negative global feedback [15][16][17][18][19]. On the contrary, antiphase oscillation may be observable with negative global feedback only and with no diffusive coupling.…”