Mechanism and model of the oscillatory electro-oxidation of methanol.

A mechanism for the kinetic instabilities observed in the galvanostatic electro-oxidation of methanol is suggested and a model developed. The model is investigated using stoichiometric network analysis as well as concepts from algebraic geometry (polynomial rings and ideal theory) revealing the occurrence of a Hopf and a saddle-node bifurcation. These analytical solutions are confirmed by numerical integration of the system of differential equations.

Model of calcium oscillations due to negative feedback in olfactory cilia.

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.

Effects of noise near a homoclinic bifurcation in an electrochemical system.

The interaction of external noise with an electrochemical oscillator (anodic dissolution of iron) has been studied experimentally on both sides of the homoclinic bifurcation. In the oscillatory regime the regularity of the limit cycle behavior was destroyed with increasing noise amplitude until no periodicity was observable any more. In contrast, the response of the excitable state (fixed point regime) became more regular at intermediate noise levels.

Birhythmicity induced by perturbing an oscillating electrochemical system.

We describe the generation of new limit cycles in electrochemical systems under the influence of external periodic perturbations. For certain specific parameters of a nonharmonic forcing function, two coexisting periodic orbits can be generated from a single limit cycle observed in the unperturbed dynamics. This inception of birhythmicity (bistability) is observed in both simulations and actual experiments involving potentiostatic electrodissolution of copper in an acetate buffer.

Theory of electrochemical pattern formation.

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.

Remote triggering of waves in an electrochemical system

In the potentiostatic electrochemical oxidation of formic acid on a platinum ring electrode under bistable conditions, an appropriate perturbation at one location of the ring can cause the emergence of a wave on the opposite side (remote triggering). These findings can be rationalized in terms of the nonlocal coupling function of the system and are theoretically reproduced by solution of the corresponding reaction-migration equation.

Chemical turbulence and standing waves in a surface reaction model: The influence of global coupling and wave instabilities.

Among heterogeneously catalyzed chemical reactions, the CO oxidation on the Pt(110) surface under vacuum conditions offers probably the greatest wealth of spontaneous formation of spatial patterns. Spirals, fronts, and solitary pulses were detected at low surface temperatures (T<500 K), in line with the standard phenomenology of bistable, excitable, and oscillatory reaction-diffusion systems. At high temperatures (T greater, similar 540 K), more surprising features like chemical turbulence and standing waves appeared in the experiments. Herein, we study a realistic reaction-diffusion model of this system, with respect to the latter phenomena. In particular, we deal both with the influence of global coupling through the gas phase on the oscillatory reaction and the possibility of wave instabilities under excitable conditions. Gas-phase coupling is shown to either synchronize the oscillations or to yield turbulence and standing structures. The latter findings are closely related to clustering in networks of coupled oscillators and indicate a dominance of the global gas-phase coupling over local coupling via surface diffusion. In the excitable regime wave instabilities in one and two dimensions have been discovered. In one dimension, pulses become unstable due to a vanishing of the refractory zone. In two dimensions, turbulence can also emerge due to spiral breakup, which results from a violation of the dispersion relation.