Synchronization of Oscillations and Propagation of Excitations in Circular and Linear Arrays of Coupled CSTRs

Abstract

Synchronizations of oscillatory regimes of the Belousov−Zhabotinskii (BZ) reaction in a circular array of three identical CSTRs coupled via symmetric passive diffusion/convection mass transfer were studied experimentally. Stability of symmetric and asymmetric phase-shifted oscillatory regimes with respect to variations of the coupling strength among the reaction cells was examined. The all-in-phase regime was found to be the only regime stable over the entire range of coupling strength values. Phase-shifted oscillatory regimes were found to be stable only within a narrow interval of very low coupling strength values. Spontaneous transitions of the phase-shifted regimes to the synchronized mode due to stochastic fluctuations of the coupling strength were observed. Numerical simulations with the four-variable Oregonator based model of the BZ reaction qualitatively confirmed the experimental findings. Propagation of an excitable response to periodic pulsed stimulations in a linear three-array of coupled chemical excitators (Belousov−Zhabotinskii reaction) was studied in dependence on the coupling strength, on the excitability level of the reaction mixture, and on the period and amplitude of pulse stimulation. Regimes of complete and partial propagation of the excitable response and the regimes of partial and complete propagation failure were observed. Numerical simulations predict qualitatively well excitatory regimes observed in experiments.

Spatially Organized Dynamical States in Chemical Oscillator Networks: Synchronization, Dynamical Differentiation, and Chimera Patterns

“…Earlier experimental studies on coupled oscillatory discrete reaction units have been conducted with coupled continuous, stirred tank reactors [ 1 ]. With a relatively small number of oscillating elements and simple networks (2-4 element chain, ring, or global configuration [ 21 – 25 ]) the transition to synchronization was described. Sixteen bistable reactors were locally coupled in a chain [ 26 , 27 ] or ring [ 28 ] geometry for studies of wave propagation failure and pinning dynamics.…”

Oregonator generalization as a minimal model of quorum sensing in Belousov–Zhabotinsky reaction with catalyst confinement in large populations of particles

“…20 These efforts yielded a variety of phenomena, including rhythm splitting, 1,3 phase-difference locking, 2,8-10,14-17 oscillator death 4,8,17,19,20 and rhythmogenesis, 5,19,20 entrained responses to pulsed forcing, 6,7,11,16 presynchronization, 14 quasiperiodicity, bursting and chaos, [10][11][12][13]15,17 or coupled chaotic states. 12,13 Moreover, investigations were also extended to three [21][22][23][24][25][26] or more interacting reactors, [27][28][29][30][31][32] offering further new insights into how these systems react to external stimuli in terms of their propagation 21,22,[27][28][29][30] or even information encoding and decoding. 31,32 Several approaches exist for studying the collective dynamics of even larger numbers of oscillators.…”

Dynamical regimes of a pH-oscillator operated in two mass-coupled flow-through reactors

“…A special case involves electrical coupling, [11][12][13][14] where the system is studied in two CSTRs, using the difference in redox potential between the two reactors to determine the amount of current which flows from one to the other as a result of chemical changes. A more commonly employed configuration realises the coupling by mass transport, usually via passive mass exchange [15][16][17][18][19] or by additional pumping. 20,21 One frequently encountered phenomenon in physically coupled systems is entrainment, in which two coupled oscillators mutually adapt their dynamics.…”