[1] Winston, D.; Arora, M.; Maselko, J.; Gáspár, V. and Showalter, K.
Cross-membrane coupling of chemical spatiotemporal patterns
Nature, 1991, 351, 132-135.Abstract. Chemical systems may communicate by exchange of common species through mass transport, and such coupling may give rise to dynamical compexity beyond that possible in the independent systems. We report here on dynamical spatiotemporal patterns across a membrane. Chemical waves appear on Nafion membranes that are loaded with ferroin catalyst and bathed in a mixture of the reagents of the Belousov-Zhabotinsky oscillatory reaction. The waves on each side of the membrane couple by diffusive transport through the membrane. The coupling initially gives rise to the spontaneous appearance of spiral waves, and subsequent behaviour reveals several distinct phases of evolution, ultimately leanding to complete spatiotemporal entrainment.
[2] Gáspár, V.; Maselko, J. and Showalter, K.
Transverse coupling of chemical waves
Chaos, 1991, 1, 435-444.Abstract. The transverse coupling of chemical waves is investigated using a model scheme for excitable media. Chemical waves supported on the surfaces of a semipermeable membrane couple via diffusion through the membrane, resulting in new types of spatiotemporal behavior. The model studies show that spontaneous wave sources may develop from interacting planar waves, giving rise to a complex sequence of patterns accessible only by perturbation. Coupled circular waves result in the spontaneous formation of spiral waves, wich subsequently develop patterns in distinct domains with characteristic features. The long time entraiment behavior of coupled spiral waves reveals regions of 1:2 phase locking.
[3] Petrov, V.; Gáspár, V.; Masere, J. and Showalter, K.
Controlling chaos in the Belousov-Zhabotinsky reaction
Nature, 1993, 361, 240-243.Abstract. Deterministic chaos is characterized by long-term unpredictability arising from an extreme sesitivity to initial conditions. Such behaviour may be undesirable, particularly for processes dependent on temporal regulation. On the other hand, a chaotic system can be viewed as a virtually unlimited reservoir of periodic behaviour which may be accessed when appropriate feedback is applied to one of the system parameters. Feedback algorithms have now been successfully applied to stabilize periodic oscillations in chaotic laser, diode, hydrodynamic and magnetoelastic systems, and more recently in myocardial tissue. Here we apply a map based, proportional-feedback algorithm to stabilize periodic behaviour in the chaotic regime of an oscillatory chemical system: the Belousov-Zhabotinsky reaction.
[4] Tóth, Á.; Gáspár, V. and Showalter, K.
Signal transmission in chemical systems: propagation of chemical waves through capillary tubes
Journal of Physical Chemistry, 1994, 98, 522-531.Abstract. The propagation of chemical waves through narrow channels has been investigated. Thin layers of excitable Belousov-Zhabotinsky mixtures are connected by precision-bore capillary tubes of different internal diameters. A wave initiated on one side of an otherwise impenetrable barrier enters and travels trough the capillary tube, forming a hemisphere of excited solution at the exit. When the tube diameter is greater than a critical value, the excitation serves to initiate a circular wave in the second compartment; otherwise, the hemisphere collapses and no wave is initiated. Electrochemically generated periodic wave trains give rise to resonance patterns characterized by firing numbers 1/n, where n = 1,2, etc. is the number of waves entering the tube for every wave exiting. The firing numbers correspond to one branch of a Farey tree; higher periodic resonances in modeling calculations indicate that more fully developed Farey sequences may also occur. A one-dimensional mapping procedure is proposed to describe the appearance and ordering of the resonance patterns.
[5] Dajka, J.; Károly, T.; Nagy, I.; Gáspár, V. and Noszticzius, Z.
Transition between Circular Fronts and Spiral Waves in Marginally Excitable Media
J. Chem. Soc. Faraday Trans., 1996, 92, 2897-2901.Abstract. Belousov-Zhabotinsky (BZ)-type waves are studied on a polysulfone membrane loaded with bathoferroin catalyst. The membrane is placed on a glass-fiber filter-disc soaked with a BZ medium containing no catalyst. Waves are periodically initiated on the membrane surface by using silver- and platinum-wire electrodes. When the area around the silver electrode is made marginally excitable by sufficiently shortening the period of perturbations, an unusual transition between circular fronts and spiral waves is observed.
[6] Kiss, I.Z.; Gáspár, V.; Nyikos, L. and Parmananda, P.
Controlling Electrochemical Chaos in the Copper-Phosphoric Acid System
J. Phys. Chem. A, 1997, 101, 8668-8674.Abstract. Model calculations indicate that chaotic current oscillations during anodic electrodissolution of copper into phosphoric acid may be controlled by applying a simple map-based algorithm. In the experiments, the unstable period-one and period-two orbits embedded in the chaotic attractor have been stabilized by small perturbations of the anodic potential. We present the results of an experimental test for a power law relating the average chaotic transient time to the size of maximum perturbation allowed during control. The reported experimental results are in good agreement with the theoretical predictions by Ott, Grebogi, and Yorke.
[7] Flesselles, J.-M.; Belmonte, A. and Gáspár, V.
Dispersion Relation for Waves in the Belousov-Zhabotinsky Reaction
J. Chem. Soc. Faraday Trans., 1998, 94, 851-855.Abstract. Analysis of a chemical model for the Belousov-Zhabotinsky reaction leads to an analytic form for the dispersion relation of waves travelling in such a medium. It is found that the velocity varies like the hyperbolic tangent of the normalized period. Data analysis suggests that the normalization time is the selected spiral period for the medium. This result agrees with previously published data, one-diemnsional as well as two-dimensional, all of which can be rescaled onto a single dimensionless curve.It thus provides a unifying approach to all waves in this reaction.
[8] Taylor, A.F.; Gáspár, V.; Johnson, B.R. and Scott, S.K.
Analysis of Reaction-Diffusion Waves in the Ferroin-Catalysed Belousov-Zhabotinsky Reaction
Phys. Chem. Chem. Phys., 1999, 1, 4595-4599.Abstract. The Oregonator model is used to analyse reaction-diffusion waves in the ferroin-catalysed Belousov-Zhabotinsky reaction. The value of the effective rate constant of ferriin reduction kJ is determined from experimental wave profiles of the oxidised catalyst obtained from solutions open to air, nitrogen, or sealed with a perspex lid. The value of kJ is found to be lower in systems affected by O2. The dependence of the wave speed c on the concentration of ferriin in the wave profiles is analysed. An alternative method for the determination of kJ from a relationship between the period of target initiation T and [Fe(III)] is presented. The effect of these results on the ‘universal dispersion relation’ is also discussed.
[9] Parmananda, P.; Madrigal, R.; Rivera, M.; Nyikos, L.; Kiss, I.Z. and Gáspár, V.
Stabilization of unstable steady states and periodic orbits in an electrochemical system using delayed-feedback control
Phys. Rev. E, 1999, 59, 5266-5271.Abstract. We report numerical and experimental results indicating successful stabilization of unstable steady states and periodic orbits in an electrochemical system. Applying a continuous delayed-feedback technique not only periodic and chaotic oscillations are suppressed via stabilization of steady-state solutions but also the chaotic dynamics can be converted to periodic behavior. In all cases the feedback perturbation vanishes as a target state is attained.
[10] Tóth, R.; Gáspár,V.; Belmonte, A.; O'Connell, M.C.; Taylor, A.F. and Scott, S.K.
Wave Initiation in the Ferroin-Catalysed Belousov-Zhabotinsky Reaction with Visible Light
Phys. Chem. Chem. Phys., 2000, 2, 413-416.Abstract. The initiation of chemical reaction-diffusions waves by visible light of wavelength l = 632.8 nm from a 20 mW He-Ne laser in the ferroin-catalysed BZ reaction on a polysulfone membrane is reported. With low loading of the catalyst on the membrane, oxidation waves can be initiated from the resting steady state and in the recovering tail of a wave. With high loading, waves can only be initiated in the ‘vulnerable’ region behind an existing wavefront. The mechanism of this initiation is discussed in terms of the photoreduction of the metal-ligand catalyst and expressed in terms of a modified Oregonator model. These new observations are in contrast to the inhibitory effect of visible light in the light-sensitive Ru-catalysed BZ system.
[11] Kiss, I.Z.; Gáspár, V. and Hudson, J.L.
Experiments on Synchronization and Control of Chaos on Coupled Electrochemical Oscillators
J. Phys. Chem. B, 2000, 104, 7554-7560.Abstract. Experiments were carried out on synchronization and control of complex chaotic dynamics observed during the dissolution of two and four coupled nickel electrodes in sulfuric acid under potentiostatic conditions. In a given potential range the individually measured currents exhibit asynchronous chaotic oscillations. The complexity (as measured by the correlation dimension) of the chaotic oscillations depends on the extent of coupling among the electrodes. Thus the effectiveness of a combined synchronization–delayed-feedback procedure can be tested on systems with increasing complexity. We show that the asynchronous chaotic oscillations can be converted to synchronized and simple, periodic current oscillations by a two-step procedure. The chaotic current oscillations of coupled electrodes are first synchronized by perturbations of external resistors that are connected individually to each electrode. Then, the desired periodic orbit is stabilized by perturbations of the potential. We also observed that certain non-vanishing perturbations could lead to only partially synchronized, so called ‘clustered’ chaotic states.
[12] Kiss, I.Z. and Gáspár, V.
Controlling Chaos with Artificial Neural Network: Numerical Studies and Experiments
J. Phys. Chem. A, 2000, 104, 8033-8037.Abstract. Although there are a number of theoretically suggested chaos control methods using Artificial Neural Networks (ANN), experimental tests are still lacking. In this paper, we report on experimental chaos control during the electrochemical dissolution of copper in phosphoric acid. The neural network implementation of simple proportional and recursive feedback algorithms are presented.
[13] Peng, B.; Gáspár, V. and Showalter, K.
False Bifurcations in Chemical Systems: Canards
Phil. Trans. R. Soc. Lond. A, 1991, 337, 275-289.Abstract. A canard is a false bifurcation in which the amplitude of an oscillatory system may change by orders of mangitude while the qualitative dynamical features remain unchanged. Recent theoretical considerations suggest that canards are characteristic of fast-slow dynamical systems and are associated with the stable and unstable manifolds of the phase plane. An alternative characterization of canard behaviour is proposed involving the crossing of an inflection line by a limit cycle growing out from an unstable stationary state. The inflection line comprises the locus of the points at which the curvature of any phase plane trajectory is zero. The role of the inflection line in the onset of canard behaviour as well as in the continuity of the transaction is examined in a two-variable model for the oscillatory EOE reaction., the Autocatalator, and in the two-variable Oregonator. The approach is also applied to the van der Pol oscillator, the system in which canard behaviour was first examined.
[14] Kéki, S.; Magyar, I.; Beck, M.T. and Gáspár, V.
Modeling the oscillatory bromate oxidation of ferroin in open systems
Journal of Physical Chemistry, 1992, 96, 1725-1729.Abstract. A model for the ferroin-bromate-bromide-sulfuric acid system in a continuously stirred (flow-through) tank reactor has been constructed by extending the Noyes-Field-Thompson mechanism with the folloving composite processes: (a) ferroin-bromate, (b) ferroin-bromous acid, (c) ferroin-hypobromous acid, (d) ferroin-bromine, (e) feriin-bromide, and (f) ferriin-bromine. The calculated high amplitude oscillations and kinetic phase diagram are in good accordance with the experiments reported earlier. By completing the scheme with a reaction step accounting for the precipitation and dissolution of a ferroin-tribromide salt, the batch oscillations found at high concentrations of reactants can also be simulated.
[15] Kiss, I.Z. and Gáspár, V.
Predicting the Dynamics of an Oligo-oscillatory Reaction by an Artificial Neural Network
ACH–Models in Chemistry, 1995, 132, 887-901.Abstract. Artificial neural networks (ANNs) are model-free computational tools that can "learn" the linear or nonlinear rules nembedded in a dataset. We report the results of an attempt to utilize ANNs in the field of reaction kinetics. A feedforward network is trained to predict the main dynamical features of oligo-oscillations in the acidic bromate—ascorbic acid—malonic acid reacting mixture, in which the concentration of bromide ion (an intermediate) shows three extrema as a function of time. Inputs to the network are the initial concentrations of reactants, while outputs are the predicted values of bromide-ion concentration and reaction time at the extrema. The network is first tested on a numerically generated dataset and then applied to experiments. The results provide evidence that ANNs can be efficiently employed for the prediction of the dynamics of complex chemical systems, especially, when the mechanism of a reaction is not fully understood.
[16] Marlovits, G.; Wittmann, M.; Gáspár, V. and Noszticzius, Z.
A new chemical oscillator in a novel open reactor: ClO2-I2-acetone system in a membrane fed stirred tank reactor
Journal of Physical Chemistry, 1995, 99, 5359-5364.Abstract. The title reaction was carried out in a new type of semibatch reactor, where iodine or both iodine and chlorinedioxide are fed to the stirred bulk of the reactor through thin and selective silicon rubber membranes. For model calculations the iodine inflow rate and the pseudo-first-order rate constant of the iodide production from iodine were determined experimentally. All other reactions and rate constants were taken from the literature. The period and the duration of the experimentally found and theoretically predicted oscillations agree rather well. An exact electrochemical interpretation of the amplitude of the electrode potential oscillations requires further research.
[17] Volford, A.; Wittmann, M.; Marlovits, G.; Noszticzius, Z. and Gáspár, V.
Platinum as a Chlorine Dioxide/Chlorite Redox Electrode in ClO2 Based Oscillating Reactions and a New Semibatch Oscillator: the ClO2-Acetone System with I- Inflow
J. Phys. Chem. B, 1997,101, 3720-3726.Abstract. A systematic study of the potential response of platinum electrode to various redox species in ClO2 based chemical oscillators proves that it is the Cl(+4)/Cl(+3) redox pair that determines the potential in these systems. According to the results reported here, the electrode potential can be predicted from known concentrations of the Cl(+4) and Cl(+3) species or, inversely, these concentrations can be estimated from the measured potential. Thus, at constant ClO2 levels the platinum behaves as a „chlorite selective” electrode. To demonstrate the feasibility of this approach, potentiometric oscillations were recorded in two different ClO2 based oscillating systems, and the experimental results were compared with potentiometric traces calculated by two alternative models.
[18] Kiss, I.Z.; Gáspár, V. and Nyikos, L.
Stability Analyis of the Oscillatory Electrodissolution of Copper with Impedance Spectroscopy
J. Phys. Chem. A, 1998, 102, 909-914.Abstract. Impedance spectroscopy is applied to quantitatively characterize the bifurcations leading to current oscillations during anodic dissolution of a copper rotating-disk electrode in sodium acetate–glacial acetic acid and o-phosphoric acid electrolytes under potentiostatic control. The line of Hopf bifurcations in a diagram spanned by the uncompensated series resistance and the true electrode potential has been constructed by measuring the linear frequency response of the electrochemical systems. On the basis of impedance data we have also determined the critical frequency by which oscillations emerge at the bifurcation points. Qualitative differences in the origin of current oscillations in the studied systems are explained by the results of experimental linear stability analysis with impedance spectroscopy.
[19] Davies, M.L.; Halford-Maw, P.A.; Hill, J.; Tinsley, M.R.; Johnson, B.R.; Scott, S.K.; Kiss, I.Z. and Gáspár, V.
Control of Chaos in Combustion Reactions
J. Phys. Chem., 2000, 104, 9944-9952.Abstract. The chaotic evolution in the combustion of CO in a well-stirred flow reactor is controlled experimentally using a modified form of the simple proportional feedback (SPF) algorithm. An unstable period-1 oscillation is stabilized through the imposition of small, appropriate perturbation which are calculated from the observed experimental response of the system and do not require any information concerning the reaction mechanism. It is observed that the algorithm is significantly more efficient if these perturbations are applied for only a fraction of the oscillatory period. A similar observation is made from a numerical study of a model for the H2 + O2 reaction and it is shown that this arises because the perturbations shift the system significantly from the attractor of the unperturbed system. The duration of the perturbation in each cycle then becomes a second control parameter and effects a higher-dimensional control algorithm in a simple manner appropriate to experimental implementation for such demanding systems. The control strategy is seen to be sufficiently robust to operate even though the system shows a marked drift over the course of the experiment. Some comments concerning strategies for the optimal implementation of SPF methods are then made.
[20] Parmananda, P.; Madrigal, R.; Rivera, M.; Kiss, I.Z. and Gáspár, V.
Resonant Control of Electrochemical Oscillations
J. Phys. Chem., 2000, accepted for publicationAbstract. We report experimental control of complex (periodic and chaotic) oscillatory dynamics in an electrochemical system by applying sinusoidal forcing. By choosing an appropriate frequency for the periodic modulation of an accessible control parameter (e.g., circuit potential) not only can the chaotic dynamics be easily converted to regular periodic behavior (controlling chaos), but also the character of the oscillatory dynamics could be altered (for example, 11 -->10). This is different from the previously reported work involving entrainment of oscillatory dynamics, since in our experiments the frequency of sinusoidal modulation is chosen such that the existing unstable dynamics are targetted and subsequently stabilised. Consequently the control signal is less then 5 % of its base value. Since resonant control strategy can be easily implemented without a complicated pre-control procedure, it seems relevant for applications to real systems.