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Electrochemical reactions exhibit autosustained oscillatory states once the appropriate parameters are applied. As shown herein, the main impact of operating a reaction in an oscillatory state is the increased efficiency. The electroxidation of CO-containing hydrogen is analyzed because its oscillating mechanism mimics the oscillator known as hidden negative differential resistance (HNDR). With that, experimental results and the thermodynamic calculations of this contribution could be extended for other HNDR oscillators such as ethanol and methanol electroxidation. The enlarged efficiency results from a smaller chemical dissipation.

Concepts from algebraic geometry (polynomial rings) can be used to determine analytically the stationary solutions in chemical reactions systems, more generally, systems of ordinary differential equations of polynomial form. The stability analysis via the Jacobian matrix often leads to complicated expressions which can hardly be analyzed. It is shown that these expressions can be simplified by forming quotient rings of the corresponding polynomial ring. The coefficients in the characteristic equation of the Jacobian can be represented by the normal forms obtained by generating the quotient rings so that their sign changes in dependence of a kinetic parameter and, hence, the stability can be determined. The procedure is illustrated using a well-known surface reaction.

Low-index plane Pt single crystal electrodes modified by submonolayer deposition of Sn have been tested for ethanol oxidation in acidic media using cyclic voltammetry and chronoamperometry. The enhancement factor for ethanol oxidation depends on both substrate crystallography and Sn coverage. The optimum coverage was found to be around 0.2, 0.25 and 0.52 for (1 0 0), (1 1 1) and (1 1 0), respectively. The enhancement factor was found to decrease in the order: Sn/Pt (1 1 0) > Sn/Pt (1 0 0) > Sn/Pt (1 1 1). On the other hand, the current density obtained at 0.4 V after 15 min of electrolysis was found to decrease in the order: Sn/Pt (1 1 0) > Sn/Pt (1 1 1) > Sn/Pt (1 0 0).

Since the current density near the edges of ribbon and disk electrodes is enhanced, the resulting stationary and non-stationary double layer potential is generally inhomogeneous in all electrochemical reactions. We investigate the impact of this edge effect induced spatial inhomogeneity on the pattern formation of the oscillatory formic acid oxidation on thin Pt ribbon electrodes. In order to be able to theoretically describe the spatiotemporal behavior of the double layer potential distribution, we derive and discuss the properties of the electrochemical ribbon coupling function for various distances of the reference electrode. The resulting reaction–migration equation is analyzed in connection with a chemical model accounting for the specific reaction mechanism of the formic acid oxidation. The interaction of structural inhomogeneity, chemically induced temporal instability and nonlocal spatial coupling due to ion migration gives rise to novel types of spatiotemporal behavior. The results compare favorably with experiments conducted so far, which are presented as well and can be explained within the framework of reaction–migration equations.

Spontaneous nucleation, pulse formation and propagation failure have been observed experimentally in CO oxidation on Pt(110) at intermediate pressures ( ≈ 10 − 2 mbar). This phenomenon can be reproduced with a stochastic model that includes temperature effects. Nucleation occurs randomly due to fluctuations in the reaction processes, whereas the subsequent damping out essentially follows the deterministic path. Conditions for the occurence of stochastic effects in the pattern formation during CO oxidation on Pt are discussed.

We present a mathematical model for calcium oscillations in the cilia of olfactory sensory neurons. The underlying mechanism is based on direct negative regulation of cyclic nucleotide-gated channels by calcium/calmodulin and does not require any autocatalysis such as calcium-induced calcium release. The model is in quantitative agreement with available experimental data, both with respect to oscillations and to fast adaptation. We give predictions for the ranges of parameters in which oscillations should be observable. Relevance of the model to calcium oscillations in other systems is discussed.

It is shown that hyperchaos of order m (i.e., with m positive Lyapunov exponents) can be generated by a single feedback circuit in n = 2m + 1 variables. This feedback circuit is constructed such that, dividing phase space into hypercubes, it changes sign wherever the trajectory passes from one hypercube into an adjacent one. Letting the negative diagonal elements in the Jacobian tend to zero, the dynamics becomes conservative. Instead of chaotic attractors, unbounded chaotic walks are then generated. Here we report chaotic walks emerging from a continuous system rather than the well known chaotic walks present in "Lorentz gas" and "couple map lattices."

Experimental observations of different spatiotemporal patterns of the interfacial potential on a bismuth modified platinum ring working electrode (WE) with different positions of the reference electrode (RE) in the electrocatalytic oxidation of formic acid are presented. For small distances between WE and RE, inhomogeneous patterns (e.g., standing waves and rotating pulses) are obtained, while synchronized oscillations (i.e., in-phase active or passive oscillations of interfacial potential) take over at larger distances between WE and RE. The results can be rationalized in terms of the geometry dependence of the non-local migration coupling.

Experimental observations of temporal dynamics in the electrocatalytic oxidation of methanol (CH3OH) on a polycrystalline platinum electrode are reported. Hidden negative differential resistance (HNDR) and instabilities of the system were investigated by means of an electrochemical impedance spectrum analysis and potential oscillations under galvanostatic control. This result could be applied for a direct methanol fuel cell (DMFC) with higher energy efficiency.

The spatial coupling in electrochemical systems is mediated by ion migration under the influence of the electric field. Since field effects spread very rapidly, every point of an electrode can communicate with every other one practically instantaneously through migration coupling. Based on mathematical potential theory we present the derivation of a generally applicable reaction-migration equation, which describes the coupling via an integral over the whole electrode area. The corresponding coupling function depends only on the geometry of the electrode setup and has been computed for commonly used electrode shapes (such as ring, disk, ribbon or rectangle). The pattern formation observed in electrochemical systems in the bistable, excitable and oscillatory regime can be reproduced in computer simulations, and the types of patterns occurring under different geometries can be rationalized. (c) 2002 American Institute of Physics.

We report experimental observations on the temporal dynamics in the electrocatalytic oxidation of formic acid (HCOOH) on a polycrystalline Pt electrode modified by deposition of bismuth. Bismuth modification significantly enhanced the current density of HCOOH oxidation, since it suppressed the poisoning branch and increased the apparent direct oxidation rate. Impedance spectroscopy and the galvanostatic scan in HCOOH oxidation on Bi/Pt exhibited a hidden negative differential resistance and a Hopf bifurcation. The electrocatalytic oxidation of HCOOH on Bi/Pt spontaneously underwent transitions from homogeneous catalytic activity to spatiotemporally inhomogeneous distributions of the interfacial electrode potential, in the form of traveling pulses of the interfacial potential.

Oscillatory rotating activation pulses on a Pt ring electrode during formic acid oxidation were externally perturbed via a trigger electrode at one location of the ring. While usual phase resetting was obtained for small perturbation amplitudes, stronger perturbations resulted in reversal of the direction of pulse motion when applied behind the pulse over a wide phase interval. The results are in agreement with simulations carried out with a reaction–migration model and can be rationalized in terms of short-range positive and long-range negative coupling.

We report experimental observations of the spatio-temporal dynamics in the electro-oxidation of formic acid on a Pt ring electrode modified by bismuth adatoms. Bismuth modification significantly enhanced the current density and it was found to considerably increase the existence range of oscillations and spatio-temporal self-organization. Hidden negative differential resistance and the existence of a Hopf bifurcation were deduced from the electrochemical impedance spectra and the occurrence of galvanostatic oscillations. The pattern formation resulted from hybrid effects of the nonlinear chemistry during formic acid oxidation and the long-range coupling of the interfacial potential induced by the chosen geometry (ring type) of the working electrode. Reversible transitions between traveling pulses and oscillating standing waves were observed when the outer potential or the formic acid concentration near the electrode were used as control parameters. Experimental results were compared with computer simulations of a reaction-migration system. The role of electrode inhomogeneities in pattern formation and the transform between patterns were discussed.

We use nonlinear signal processing techniques, based on artificial neural networks, to construct a continuous-time model (set of ordinary differential equations, ODEs) from experimental observations of mixed-mode oscillations during the galvanostatic oxidation of hydrogen on platinum in the presence of bismuth and chloride ions. The data was in the form of time-series of the potential for different values of the applied current and chloride ion concentration. We use the model to reconstruct the experimental dynamics and to explore the associated bifurcation structures in phase-space. Using numerical bifurcation techniques we locate stable and unstable periodic solutions, calculate eigenvalues, and identify bifurcation points. This approach constitutes a promising data post-processing procedure for investigating phase-space and parameter space of real experimental systems; it allows us to infer phase-space structures which the experiments can only probe with limited measurement precision and only at a discrete number of operating parameter settings. For example, the fitted model suggests the existence of a sub-critical Hopf bifurcation near the range of parameters probed in the experiments; this might explain the experimental difficulty in locating small amplitude simple oscillations.

We consider a comprehensive classification scheme of oscillatory electrochemical systems with respect to the mechanistic basis of their kinetic instability. Four principal oscillator categories are distinguished depending on the mechanistic role of the potential drop across the electrode ∣ electrolyte interface (double layer potential) and of the chemical species involved. In a comparative characterization, the typical experimental behavior of the four oscillator categories is described when subjected to various identification tests such as stationary and scanned cyclic voltammetric profiles, bifurcation behavior, impedance spectra and feedback control methods. It is shown that each category corresponds to a specific class of kinetic prototype models. Experimental example systems as well as numerical models taken from the literature are discussed in the context of their corresponding oscillator class. Moreover, an operational experimental procedure for a systematic mechanistic categorization of an unknown electrochemical oscillator is proposed. It is argued that an initial mechanistic categorization significantly facilitates the subsequent clarification of the relevant chemical steps of the unknown electrochemical oscillator.

Turing-like patterns formed during the polymerization of acrylamide in the presence of sulfide, methylene blue and molecular oxygen are presented. We propose a chemical model of the polymerization of acrylamide in the presence of sulfide and oxygen. The model explains the formation of Turing patterns in this system. The experimental process of pattern formation becomes light sensitive if methylene blue is added. A space-periodic perturbation may thus be introduced into the system and spatial entrainment effects can be studied. The perturbation was realized by imposing an illumination pattern upon the reactive layer: after mixing the gel components and the MBO system in a Petri dish, a mask made of transparent film was placed between the light source and the dish. At different perturbation wavelengths we observed synchronization with the perturbation as well as irregular responses.

The electrochemical deposition of Ru on Pt(111) electrodes has been investigated by electron diffraction, Auger spectroscopy, and cyclic voltammetry in a closed UHV transfer system. At small coverages Ru formed a monatomic commensurate layer, at higher coverage mostly small islands with a bilayer height were detected. When the Pt was almost completely covered by Ru, three-dimensional clusters developed. The island structure of Ru changed upon electrooxidation of CO, reflecting an enhanced mobility of Ru. Adsorption and electrooxidation of CO have been studied on such Ru-modified Pt(111) electrodes using cyclic voltammetry and in situ FTIR spectroscopy. Compared to the pure metals, the Ru−CO bond is weakened, the Pt−CO bond strengthened on the modified electrodes. The catalytic activity of the Ru/Pt(111) electrode toward CO adlayer oxidation is higher than that of pure Ru and a PtRu alloy (50:50). It is concluded that the electrooxidation of CO takes place preferentially at the Ru islands, while CO adsorbe...

We report the suppression of spatiotemporal chaos observed in a spatially extended chemical system. In one spatial dimension, under appropriate parameter conditions the model system exhibits transition to turbulence via backfiring of pulses. Suppression is achieved using different feedback and forcing techniques, some of which are applicable in actual experimental situations. Results from the application of some of these strategies to a single (uncoupled) oscillator (two-dimensional O.D.E (ordinary differential equations) system) are presented to demonstrate similarities in the dynamical response of a single system and an extended system under the influence of external feedbacks.

An experimental and theoretical description of the oscillatory electrocatalytic iodate reduction system in alkaline solution is presented. Experimental measurements suggested the crucial role of a negative differential resistance as well as the presence of hydrogen evolution in the oscillatory instability. A simple kinetic model with one chemical species was developed which involved: (i) an iodate reduction current with N-shaped potential dependence due to a Frumkin repulsion effect; and (ii) an additional ‘iodate-independent’ current providing process. The dynamical behavior of the model compares favorably with experiments as far as voltammetric profiles, stirring effects and bifurcations between stable and oscillatory states are concerned. It is further shown that the model can account for oscillatory states in a number of related electrocatalytic systems.

The underpotential deposition (UPD) of copper on to Pt(111) in the presence of chloride anions was studied by full-dynamical LEED-intensity analyses. A deformed (4×4) LEED pattern was observed at an emersion potential of 0.36 V vs. Ag/AgCl, right in between the two characteristic and well-separated peaks of the cyclic voltammogram (CV). Corresponding LEED intensity measurements and simulations of the integral-order beams indicate that the UPD of Cu forms a single pseudomorphic Cu layer on Pt(111).

Derivative control was applied to electrochemical oscillators under potentiostatic as well as galvanostatic conditions; i.e., the time derivative of a measured quantity (such as the current or the concentration of an electrochemical species) is fed back to the externally applied voltage or, respectively, current. In particular cases the control led to stabilization of the unstable node, i.e., suppression of oscillations. By comparison with model calculations, it is shown that the result of the derivative control provides valuable information about the mechanism of an electrochemical oscillator and the role of certain species.

Herein, oscillatory formic acid (FA) electrooxidation on polycrystalline palladium is investigated and compared with the one on polycrystalline platinum; major differences between both are attributed to differences on the kinetics of sub-set chemical network as well as to preferential routes admitted on palladium surface. To presume the kinetic rate of poison accumulation on palladium, FA oxidation was accomplished in presence of occluded hydrogen and hydrogen-free electrodes. The preferential routes were presumed from the temporal pattern. Markedly, oscillations during FA electrooxidation have minimum potential at 0.2 V, which is linked to the fast rate of direct dehydrogenation; moreover, it has one of the largest induction period (ca. 60 min) and oscillatory period (20 min) observed in electrochemistry, since subsurface hydrogen slows down the rate of CO accumulation on the surface. Neste trabalho, a eletrooxidação oscilatória de ácido fórmico (FA) é investigada sobre paládio policristalino e comparada a resultados obtidos sobre platina policristalina; as principais diferenças entre ambas as superfícies são atribuídas a diferentes cinéticas da sub-rede química tanto quanto a rotas preferenciais admitidas sobre a superfície de paládio. Com o intuito de presumir a taxa cinética de acumulação de veneno sobre paládio, eletrooxidação de FA foi conduzida na presença e ausência de hidrogênio dissolvido na rede cristalina do paládio. As rotas preferenciais foram presumidas a partir do padrão temporal (série temporal). Notoriamente, oscilações de potencial durante a eletrooxidação de FA possuem mínimo de potencial em 0,2 V, o que é associado a uma rápida taxa de desidrogenação direta; além disso, períodos de indução (ca. 60 min) e oscilação (20 min) estão entre os mais compridos já observados em eletroquímica, pois o hidrogênio incluso na rede cristalina do paládio reduz a taxa de acumulação de CO sobre a superfície.

We address the stability of solitary pulses as well as some other traveling structures near the onset of spatiotemporal chaos in a two-species reaction-diffusion model describing the oxidation of C ...

A kinetic model is developed for the electrocatalytic oxidation of formic acid on Pt under potentiostatic control. The model development proceeds stepwise via a simple model of the electrocatalytic CO oxidation. The full model consists of four coupled, nonlinear ordinary differential equations. The scanned and stationary current/outer potential (I/U) behavior, stationary current oscillations, two-parameter bifurcation diagrams and stirring effects are simulated using realistic model parameters. The numerical findings are found to be consistent with the experimental results given by Strasser et al. The model reproduces period-1 as well as mixed-mode oscillations. Furthermore, a mechanistic analysis of the model was performed: two suboscillators are identified whose characteristics allow a plausible interpretation of the observed dynamics. After a classification of the suboscillators into previously described categories, an attempt is made to identify the minimal mechanistic requirements for electrochemical current oscillations.

The experimental characterization of the current/outer potential (I/U) behavior during the electrochemical CO oxidation on Pt(100), Pt(110) and Pt(111) is used as the first step towards a thorough investigation of the processes occurring during the electrochemical formic acid oxidation. The CO study is followed by new cyclovoltammetric results during the electrochemical formic acid oxidation on the corresponding Pt single crystals. At high concentrations of formic acid, the cyclovoltammograms revealed a splitting of the large current peak observed on the cathodic sweep into two peaks whose dependence on scan rate and reverse potential was investigated. It turned out that the presence of a sufficiently large ohmic resistance R was crucial for oscillatory instabilities. Given an appropriate resistance, all three Pt surfaces were found to exhibit current oscillations at both low and high formic acid concentrations. On Pt(100) stable mixed-mode oscillations were observed. In addition, the sensitivity of the oscillations to stirring was investigated. Whereas the period-1 oscillations were found to be independent of stirring, the mixed-mode oscillations transformed into simple oscillations with stirring. The mechanism giving rise to instability and oscillations is described.

We report the suppression of spatiotemporal chaos observed in coupled map lattices. Suppression is achieved using different feedback techniques, most of which are applicable to actual experimental situations. Results from application of feedback control to a single chaotic element (single map) are presented to demonstrate similarities in the dynamical response of a single system and an extended system under the influence of external feedback.

Sufficient and necessary conditions for the occurrence of a Hopf bifurcation in chemical reaction mechanisms are presented using the formalism of stoichiometric networks. The conditions are applied to determine the mechanistic basis of chemical oscillations in isothermal surface reactions. Realistic examples are given for the different oscillatory mechanisms.

A recently proposed model to describe the galvanostatic oscillating oxidation of hydrogen on Pt in the presence of copper and chloride is also able to explain the potentiostatic behaviour of the experimental system. For sufficiently high series resistance it exhibits current oscillations on a branch where the stationary current-voltage curve has a positive polarization slope. This is in contrast to most of the potentiostatic oscillators examined and described previously, where the oscillations are caused by an interplay between the IR drop and a region of negative polarization slope. The mechanism is discussed and compared with other models which describe potentiostatic oscillators. The main difference is shown to lie in the existence of a hidden negative impedance, which is detected experimentally by impedance spectroscopy.

Experiments with an anisotropic chemical excitable medium---a catalytic chemical reaction on a single crystal surface---reveal a kind of stable wave pattern representing single traveling-wave fragments. Their existence is attributed to the presence of a strong state-dependent diffusion anisotropy in the medium. A simple theory of traveling fragments setting general conditions for their observation is proposed. Its conclusions are confirmed by numerical simulations of a reaction-diffusion model. Our analysis suggests that traveling-wave fragments are a general property of excitable media with strong state-dependent anisotropy.

The dynamics of a large number of heterogeneously catalyzed reactions have been studied under a variety of conditions using different catalysts and reactor designs. Experiments with single crystal surfaces at low pressure are required in order to elucidate the underlying elementary chemical steps. Here we present a case study of such an approach using the isothermal CO oxidation on a Pt(110) surface. Surface science experiments allow to construct a simple but realistic reaction-diffusion model capable of reproducing the experimentally observed spatiotemporal patterns, representative examples of which are described.

A simple model of the galvanostatic oscillations that occur during the oxidation of hydrogen at platinum electrodes in the presence of electrosorbing metal ions and specifically adsorbing anions is presented. It consists of three ordinary differential equations describing the degree of coverage of the electrode with underpotential-deposited metal and with specifically adsorbed anions; the third variable is the potential drop across the double layer. This model is able to reproduce the potentiostatic experiments of the system. The galvanostatic behavior is examined by integration of the equations and by bifurcation analysis. The experimental dependence on the control parameters is reproduced in all main features. The parameters were altered to check the model for robustness and to determine the essential processes leading to oscillations. Mixed-mode and period-doubled oscillations were also found. Inclusion of a fourth variable, the concentration of metal ions in front of the electrode, leads to a better quantitative description of oscillations at low metal ion concentrations.

Rigidly rotating spiral waves under constant external parameters, drifting spirals under the influence of a periodic perturbation as well as turbulent patterns have been observed in the isothermal CO oxidation on a Pt(1 1 0) single crystal surface. A simple reaction-diffusion model can reproduce these findings. It is pointed out that the spiral resonances depend on the symmetry of the surface. The mechanism leading to turbulence is briefly described.

We studied the oscillatory galvanostatic Hg-oxidation on the three low-index Pt surfaces in the presence of Cu 2+ and different electrolytes: H 2 SO 4 , H 2 SO 4 +Cl - and H 2 SO 4 +Br - . It was found that both surface orientation of the Pt-electrode as well as the nature of the anions strongly influence the dynamics. Halide ion adsorption plays an essential role for the occurrence of oscillations; their binding strengths on the different single-crystal electrodes correlate with the dynamic behaviour of the respective system. The reaction was further investigated using ring-disk electrodes (Pt/Pt and Pt/Au). This allowed the quantitative determination of the change of the copper coverage and the Hg-current during oscillations as well as their phases relative to the electrode potential. From these studies a simple three-variable model (taking into account the coverages of copper and anions as well as the potential) was deduced, based on competitive adsorption of halides and Cu. The model explains the occurrence of oscillations and predicts the correct phase relationships of the oscillating variables

The problem of non-stationarity in experimentally recorded time-series is common in many (electro)chemical systems. Underlying this non-stationarity is the slow drift in some uncontrollable parameter, and it occurs in spite of the fact that all controllable parameters are kept constant. Particularly for electrochemical systems, some of us have recently suggested [J. Phys. Chem. C, 144, (2010), 22262–22268] an empirical method to stabilize experimental time-series. The method was exemplified for the electro-oxidation of methanol and different patterns were satisfactorily stabilized. In this paper we further elaborate some mechanistic aspects of this method and test it for the electro-oxidation of formaldehyde, a system that has some resemblance with the electro-oxidation of methanol, but produces a richer dynamics. In terms of the reaction mechanism, we were able to describe the coupling and to separate the surface processes of the two sub-systems: the fast one (or the core-oscillator) and the slow one, responsible for the drift.

In the reduction of NO with H2 on a Rh(110) surface rectangularly shaped target patterns and spirals with sharp corners have been observed. These patterns can be reproduced with a simple model assuming that the (anisotropic) diffusion is state dependent. Such a dependence is realized in the system Rh(110)/NO + H2 by the presence of different adsorbate-induced reconstructions with varying substrate geometries.

Kinetic investigations in the oscillatory state have been carried out in order to shed light on the interplay between the complex kinetics exhibited by a proton exchange membrane fuel cell fed with poisoned H(2) (108 ppm of CO) and the other in serie process. The apparent activation energy (E(a)) in the stationary state was investigated in order to clarify the E(a) observed in the oscillatory state. The apparent activation energy in the stationary state, under potentiostatic control, rendered (a) E(a) ≈ 50-60 kJ mol(-1) over 0.8 VE0.6 V and (b) E(a) ≈ 10 kJ mol(-1) at E = 0.3 V. The former is related to the H(2) adsorption in the vacancies of the surface poisoned by CO and the latter is correlated to the process of proton conductivity in the membrane. The dependence of the period-one oscillations on the temperature yielded a genuine Arrhenius dependence with two E(a) values: (a) E(a) around 70 kJ mol(-1), at high temperatures, and (b) E(a) around 10-15 kJ mol(-1), at lower temperatures. The latter E(a) indicates the presence of protonic mass transport coupled to the essential oscillatory mechanism. These insights point in the right direction to predict spatial couplings between anode and cathode as having the highest strength as well as to speculate the most likely candidates to promote spatial inhomogeneities.

A refined version of the Sano-Sawada algorithm to compute Lyapunov spectra has been implemented and tested with several models, which include periodic, chaotic and hyperchaotic attractors, under conditions designed to mimic experimental situations. It was found that reliable Lyapunov exponents can be obtained for time series of moderate length and point density, also in the presence of interactive noise as long as its amplitude does not exceed ≈ 1% of the oscillation amplitude. The algorithm was then applied to experimental data from the CO oxidation on Pt(110), clearly showing the occurrence of chaos as well as hyperchaos.

The dynamic behavior of the electrocatalytic oxidation of hydrogen on a platinum anode in the presence of Cu 2+ and Cl − ions under galvanostatic conditions has been studied experimentally in two control parameters: current density and copper ion concentration. This parameter plane can roughly be divided into three broad regions: A steady state is found at low values of the current density, at medium values the system shows small amplitude oscillations, whereas at high current densities typical mixed mode oscillations (MMOs) are found. Depending on the Cu 2+ concentration, the transition from the small amplitude to the mixed mode regime takes place from a simple periodic, period doubled, or chaotic attractor arising from a Feigenbaum route. In this paper we focus on the characteristics of these different transitions to MMOs and try to construct a bifurcation diagram. The bifurcation from the small chaotic attractor to MMOs very likely constitutes an interior crisis (a bifurcation at which the small chaotic attractor is destroyed by colliding with a stable manifold of a saddle type limit set). At lower copper ion concentrations, the transition to MMOs moved through the period-double cascade. We compile different properties of the bifurcation diagram and discuss a scenario which fits the observations in a consistent way.

A dynamic model designed to describe bistability and kinetic oscillations of the reaction rate during the oxidation of CO on a Pt(110) single crystal surface is extended by incorporating surface diffusion of adsorbed CO in order to analyze the properties of traveling waves propagating on the catalytically active surface. In the range of control parameters (partial pressure of oxygen and carbon monoxide and temperature) which corresponds to excitable dynamics, solitary pulses and periodic wave trains can be triggered. Using both asymptotic and numerical methods, the velocity and shape of the pulses as well as the dispersion relation for periodic wave trains are determined and compared to experimental data where available.

A kinetic model of the catalytic CO oxidation on a Pt(110) surface is used to describe effects of spatiotemporal self-organization, which have been observed experimentally with this system. After some simplification and taking advantage of the strong separation of fast and slow variables the model can be used to obtain analytical expressions for front and pulse velocities, pulse width and the dispersion relation, as well as for the dependency of pinned spiral rotation on the core size. Comparison with experimentally observed wave velocities and spiral rotation allows to draw conclusions about defects on the surface. Possible extensions of the model in order to explain more complex spatiotemporal behavior are briefly discussed.

The periodically perturbed oscillations in the isothermal CO oxidation on a Pt(110) surface at low pressure were modeled using the recently developed reconstruction model of kinetic oscillations, in which the usual Langmuir–Hinshelwood mechanism is coupled with the CO‐driven 1×2⇄1×1 phase transition of the surface. The experimental findings (entrainment bands, quasiperiodicity, critical slowing down) could be well reproduced with this model. The calculations revealed a complicated bifurcation fine structure of the Arnol’d tongues. While the skeleton structure turned out to be the same as in other studies, some additional features were found, and several details (mainly in the p/2 tongues) were different from forced systems examined previously. A co‐dimension‐3 bifurcation (in which a second‐order resonance coincides with a degenerate period doubling) is discussed in this context.

The parameters entering the kinetics for the mechanism of catalytic CO oxidation have been adapted for a Pt(110) surface, giving rise to a two‐variable model correctly predicting bistability. Oscillations are obtained when, in addition, the adsorbate‐driven 1×2–1×1 structural phase transition of Pt(110) is taken into account. Mixed‐mode oscillations can be qualitatively explained by including the faceting of the surface as a fourth variable. The limitations of the model essentially stem from the fact that only ordinary differential equations have been analyzed so far neglecting spatial pattern formation. It is discussed which dynamic phenomena observed experimentally in the CO oxidation on Pt(110) will probably not be adequately describable without taking spatial effects into account.