Dynamics of a 1D array of inhibitory coupled chemical oscillators in microdroplets with global negative feedback.

Abstract

We have investigated the effect of global negative feedback (GNF) on the dynamics of a 1D array of water microdroplets (MDs) filled with the reagents of the photosensitive oscillatory Belousov-Zhabotinsky (BZ) reaction. GNF is established by homogeneous illumination of the 1D array with the light intensity proportional to the number of BZ droplets in the oxidized state with the coefficient of proportionality ge. MDs are immersed in the continuous oil phase and diffusively coupled with the neighboring droplets via inhibitor Br2 which is soluble in the oil phase. At chosen concentrations of the BZ reactants, illumination suppresses the BZ oscillators. Without GNF, or at a very small ge < 0.29, local inhibitory coupling leads to out-of-phase oscillations of the neighboring BZ droplets with an almost constant phase shift Δφ between them, which makes a space-time plot of the BZ MDs look like a staircase. At 0.3 < ge < 0.6, regular oscillatory clusters consisting of distant BZ MDs (mostly 5-6 phase clusters) emerge. At 0.6 ≤ ge ≤ 1.0, chaotic clusters are observed. At 1.2 < ge < 1.8, regular (mostly 3-4-phase) clusters emerge again. At 1.8 < ge < (3-4), complex clusters with different (but multiple) periods of oscillation are observed. At the same time, some droplets stop oscillating. At large enough ge (>4), in the region of two-phase clusters (with several suppressed BZ MDs), final patterns seem to resemble the initial patterns. Intensive computer simulations with the ordinary differential equations support experimental results.