Spatiotemporal patterns in simple reaction cell arrays with time delay

Dolnik, Miloš; Košek, Juraj; Votrubova, V.; Marek, M.

doi:10.1021/j100065a028

Cited by 9 publications

(6 citation statements)

References 8 publications

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“…12 The effect of time delay ͑and coupling strength͒ on excitation circulating over coupled cells has also been studied. 15 In our system, time delay is introduced through the diffusion of species w across the gap.…”

Section: Introductionmentioning

confidence: 99%

Diffusive instabilities in heterogeneous systems

Vanag

Epstein

2003

The Journal of Chemical Physics

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We investigate the behavior of a system composed of two small identical water droplets loaded with an activator-inhibitor system possessing only a single stable steady state and coupled through a third, ''signaling'' species able to diffuse through the interdroplet medium. Depending on whether the third species is coupled to the activator or the inhibitor, the system can exhibit wave instability, which is equivalent to out-of-phase oscillations, or Turing instability, which is equivalent to the birth of two new stationary steady states. For a large interdroplet gap, equivalent to a large time delay, droplets can undergo synchronous, in-phase oscillations. Our analysis can be extended to a system of many coupled in-line droplets, as we illustrate.

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Section: Introductionmentioning

confidence: 99%

Diffusive instabilities in heterogeneous systems

Vanag

Epstein

2003

The Journal of Chemical Physics

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“…The PECs obtained from the analysis of the response of an excitable system to single perturbations at various phases of the excitation cycle enabled precise prediction of the behavior of the system affected by periodic perturbations. The analysis of spatiotemporal patterns of excitations in arrays of coupled reaction cells with time delay was the subject of another study …”

Section: Introductionmentioning

confidence: 99%

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

et al. 1997

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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.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Pešek

Schreiberová

Schreiber

2011

Phys. Chem. Chem. Phys.

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We present results of experiments focused on emergent and cooperative dynamics in a system of two coupled flow-through stirred reaction cells with diffusion-like mass exchange and a strongly nonlinear chemical reaction between hydrogen peroxide and thiosulphate catalysed by cupric ions in diluted solution of sulphuric acid. Due to complex mechanism, in which a crucial role is played by hydrogen and/or hydroxide ions, dynamics in a single cell entail multiple stationary states, excitability and oscillations conveniently indicated by measuring pH. When coupled, the system shows a plethora of dynamical regimes depending on the coupling strength and flow rate. Under certain conditions both cells display dynamics close to that in the absence of coupling, but majority of the regimes are emergent and cannot be deduced from dynamics of decoupled reactors. The most prominent is a stationary state maintaining highly acidic values of pH in one of the reactors and weakly acidic in the other. When each cell is set to display excitability and the coupled system is externally perturbed, the cells may cooperate and transmit excitations elicited by pulsed perturbations in one cell to the other. Periodic pulses induce firing patterns marked by a various degree of propagated excitations and by being periodic or irregular.

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Spatiotemporal patterns in simple reaction cell arrays with time delay

Cited by 9 publications

References 8 publications

Diffusive instabilities in heterogeneous systems

Diffusive instabilities in heterogeneous systems

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

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

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