17802 Phys. Chem. Chem. Phys., 2011, 13, 17802–17808 This journal is c the Owner Societies 2011 Cite this: Phys. Chem. Chem. Phys., 2011, 13, 17802–17808 Complex organizing centers in groups of oscillatory particles M. R. Tinsley,* a A. F. Taylor, b Z. Huang a and K. Showalter* a Received 28th June 2011, Accepted 17th August 2011 DOI: 10.1039/c1cp22109d We investigate the origin and evolution of spatiotemporal complexity in a system of locally coupled Belousov–Zhabotinsky chemical oscillators. Using a combination of high resolution microscopy and fine grain numerical modeling, we demonstrate that the behavior arises from an initial phase heterogeneity of the oscillators. This heterogeneity produces wave breaks in the system with the free ends becoming pinned to holes in the medium. The fastest of these pinned tips behave as reentrant circuits that phase set the rest of the medium. The slower tips are repeatedly destroyed and then re-created by the central circuit. The resulting spatiotemporal pattern repeats with the frequency of the reentrant circuit, with its spatial structure depending on the location of the initial wave breaks. 1. Introduction Local coupling within groups of oscillators often gives rise to propagating waves of activity. The resulting spatiotemporal behaviors have generated great interest due to their functional role in biological systems, such as electro-mechanical wave propagation through heart tissue 1 and cAMP waves directing the movement of starving Dictyostelium discoideum cells. 2,3 The Belousov–Zhabotinsky (BZ) reaction 4,5 is an experimentally tractable oscillatory system that has been widely used to develop an understanding of spatiotemporal patterns. 6–8 The reaction is typically studied in quasi-2D continuous media; 7,9 however, many spatiotemporal systems are composed of discrete cellular oscillators. A discretized chemical oscillator system has been developed from the BZ reaction, 10 in which the catalyst for the reaction is immobilized on individual ion-exchange particles, with each particle capable of acting as an independent oscillator in a catalyst-free BZ medium. The discrete BZ particle system has been used to investigate a wide range of dynamical behavior, including oscillator entrainment, 11,12 spiral waves on spheres, 13,14 target to spiral wave transitions, 10,15,16 and synchronization in globally and locally coupled oscillators. 17–20 Biological systems of coupled oscillators are typically heterogeneous. The role of different types of heterogeneities in wave breakages, such as spatial variations of cellular density or cellular coupling, has been extensively studied in heart tissue to better understand cardiac arrhythmias. 21–23 Early experiments on layers of catalyst particles in the BZ system reported increasing complexity of the spatiotemporal patterns with increasing bromate concentration. 10 Explanations of the origin of complex behavior in heterogeneous media such as the BZ-particle system involve the initial excitability, 15 refractory period heterogeneity, 15,24 and the presence of either inactive particles 16 or permanently excited particles. 18 Recent studies of the spontaneous appearance of wave behavior in spatial groups of nonoscillatory excitable particles have found primarily unbroken target waves, although spiral waves were occasionally observed. 25 In groups of oscillatory particles, however, complex spiral behavior from broken waves is observed. In this paper, we study the critical heterogeneity that leads to spontaneous wave breaks and spiral wave activity in spatially distributed oscillatory BZ particles. We use high resolution microscopy combined with fine grain modeling of the individual particles. Our results demonstrate that the complex patterns arise primarily from an initial phase hetero- geneity, and the resulting spatiotemporal activity is driven by reentrant circuits positioned within the medium. A reentrant circuit is an organizing center consisting of a wave of activity that repeatedly circumnavigates a defect in the medium, such as a hole. 2. Experimental details The particles used in the experiment are porous cation-exchange beads (Biorad 50WX-100, mean diameter B280 mm) that are loaded with the BZ catalyst ferroin ([Fe(phen) 3 2+ ]= 1.7  10 5 mol g 1 particles). The loaded particles are placed into a Petri dish and covered with catalyst-free BZ solution, 17,25 with [NaBr] = 0.1 M, [CH 2 (COOH) 2 ] = 0.2 M, [H 2 SO 4 ] = 0.6 M, and varied bromate concentration. The particles are uniformly illuminated from below and viewed from above using a microscope fitted with a digital camera. The bromate concen- tration is selected so that the individual particles are oscillatory, [BrO 3  ] Z 0.42 M, with the mean period of the particles a C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, WV 26506, USA. E-mail: Mark.Tinsley@mail.wvu.edu, Kenneth.Showalter@mail.wvu.edu b Department of Chemistry, University of Leeds, Leeds LS2 9JT, UK PCCP Dynamic Article Links www.rsc.org/pccp PAPER Published on 13 September 2011. Downloaded by West Virginia University Libraries on 02/06/2015 19:20:31. View Article Online / Journal Homepage / Table of Contents for this issue