Dynamical Patterns in Arrays of Coupled Chemical Oscillators and Excitators

Abstract

Dynamical regimes arising due to mutual interactions of oscillatory and excitatory modes of the Belousov-Zhabotinskii (BZ) reaction in a two-array and linear and circular three-arrays (with different arrangements of intrinsic connections) of identical continuous stirred tank reactors (CSTRs) coupled via symmetric passive diffusion/convection mass exchange were studied both experimentally and by numerical simulations. The coupling strength among individual CSTRs and the threshold of excitability of the BZ reaction mixture were varied systematically. Firing numbers (vectors) were used for classification of observed oscillatory-excitatory modes. Full spectra of firing numbers ranging from 0 to 1 were detected in all CSTR arrays investigated in experiments. The numbers of oscillators and excitators, threshold of excitability, and the way of coupling and coupling strengths within the array are principal factors affecting firing patterns of the array. Numerical simulations with the dimensionless three-variable Oregonator based model of the BZ reaction predict qualitatively well dynamical regimes encountered in experiments. Noisy coupling among the individual CSTRs due to hydrodynamical fluctuations is suggested to explain some of the observed differences.

Restoring oscillatory behavior from amplitude death with anti-phase synchronization patterns in networks of electrochemical oscillations

“…With the networks, further questions arise, e.g., what are the typical synchronization patterns or which types of network topologies can support AD or OD behavior. Important examples of chemical networks include BZ reactor systems, [22][23][24] BZ droplets, [25][26][27][28] BZ beads, [29][30][31][32][33] and chemomechanical 34 and electrochemical units. [35][36][37][38][39][40][41] Three globally coupled periodic oscillatory BZ reactors have been shown to exhibit the OD behavior.…”

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.…”

Transport limited pattern formation in catalytic fluid–particle systems

“…McDonald and Schmitz (1991) found complex bifurcation diagrams and large steady-state multiplicity in two and four interacting catalyst pellets that are aligned in a single column along the axis of a tubular reactor for a first-order exothermic reaction and mixing-cell description of the fluid flow. Dolnik et al (1994), Nevoral et al (1997) and Votrubova et al (1998) studied spatiotemporal patterns in several simple cell arrays (CSTRs interconnected by means of mass and/or information exchange) for the Belousov-Zhabotinskii and chlorine dioxide-iodide reaction kinetics models. Pawlicki and Schmitz (1987) and Sant and Wolf (1987) observed experimentally stationary temperature patterns on catalyst disks or ribbons suspended in a gas.…”