title: Phase-lag synchronization in networks of coupled chemical oscillators.
abstract: Chemical oscillators with a broad frequency distribution are photochemically coupled in network topologies. Experiments and simulations show that the network synchronization occurs by phase-lag synchronization of clusters of oscillators with zero- or nearly zero-lag synchronization. Symmetry also plays a role in the synchronization, the extent of which is explored as a function of coupling strength, frequency distribution, and the highest frequency oscillator location. The phase-lag synchronization occurs through connected synchronized clusters, with the highest frequency node or nodes setting the frequency of the entire network. The synchronized clusters successively "fire," with a constant phase difference between them. For low heterogeneity and high coupling strength, the synchronized clusters are made up of one or more clusters of nodes with the same permutation symmetries. As heterogeneity is increased or coupling strength decreased, the phase-lag synchronization occurs partially through clusters of nodes sharing the same permutation symmetries. As heterogeneity is further increased or coupling strength decreased, partial synchronization and, finally, independent unsynchronized oscillations are observed. The relationships between these classes of behavior are explored with numerical simulations, which agree well with the experimentally observed behavior.
authors.affiliation: Institut für Theoretische Physik, EW 7-1, TU Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany.
authors.forename: Jan F
authors.initials: JF
authors.lastname: Totz
authors.affiliation: C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26505-6045, USA.
authors.forename: Razan
authors.initials: R
authors.lastname: Snari
authors.affiliation: C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26505-6045, USA.
authors.forename: Desmond
authors.initials: D
authors.lastname: Yengi
authors.affiliation: C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26505-6045, USA.
authors.forename: Mark R
authors.initials: MR
authors.lastname: Tinsley
authors.affiliation: Institut für Theoretische Physik, EW 7-1, TU Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany.
authors.forename: Harald
authors.initials: H
authors.lastname: Engel
authors.affiliation: C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26505-6045, USA.
authors.forename: Kenneth
authors.initials: K
authors.lastname: Showalter
mesh_terms: D003198:Computer Simulation; D008956:Models, Chemical; D010507:Periodicity; D055668:Photochemical Processes