Bistable kinetics

V. P. Zhdanov and B. Kasemo, Bistable kinetics of simple reactions on solid surfaces lateral interactions, chemical waves, and the equistabil-ity criterion, Physica D, 70 (1994) 383. 

In addition to bistability and hysteresis, the minimal model of glycolysis also allows nonstationary solutions. Indeed, as noted above, one of the main rationales for the construction of kinetic models of yeast glycolysis is to account for metabolic oscillations observed experimentally for several decades [297, 305] and probably the model system for metabolic rhythms. In the minimal model considered here, oscillations arise due to the inhibition of the first reaction by its substrate ATP (a negative feedback). Figure 24 shows the time courses of oscillatory solutions for the minimal model of glycolysis. Note that for a large... 

A typical chemical system is the oxidative decarboxylation of malonic acid catalyzed by cerium ions and bromine, the so-called Zhabotinsky reaction this reaction in a given domain leads to the evolution of sustained oscillations and chemical waves. Furthermore, these states have been observed in a number of enzyme systems. The simplest case is the reaction catalyzed by the enzyme peroxidase. The reaction kinetics display either steady states, bistability, or oscillations. A more complex system is the ubiquitous process of glycolysis catalyzed by a sequence of coordinated enzyme reactions. In a given domain the process readily exhibits continuous oscillations of chemical concentrations and fluxes, which can be recorded by spectroscopic and electrometric techniques. The source of the periodicity is the enzyme phosphofructokinase, which catalyzes the phosphorylation of fructose-6-phosphate by ATP, resulting in the formation of fructose-1,6 biphosphate and ADP. The overall activity of the octameric enzyme is described by an allosteric model with fructose-6-phosphate, ATP, and AMP as controlling ligands. 

Dewel, G., Borckmans, P., and Walgraef, D. (1984). Relaxation kinetics in a bistable chemical system. J. Phys. Chem., 88, 5442-5. 

A simple model that makes it possible to describe optical bistability in a variety of systems is a plane nonlinear Fabry-Perot interferometer, filled with a medium whose refractive index is intensity dependent [106]. The slow kinetics of a... 

In the experiments we have used two approaches. First, we have simulated the kinetics of a bistable optical system in the Debye relaxation appoximation for different forms of potential by means of electronic analog simulation. Secondly, we have investigated the kinetics of a double-cavity membrane system (DCMS) driven by two modulated laser beams at different wavelengths. This system is known to display optical bistability [111]. 

One of the most important general features of fluctuations in a bistable system is the onset of a narrow zero-frequency spectral peak for parameter values lying in the range of the kinetic phase transition. This peak arises from... 

More generally, the surface can (for certain sets of parameters) be in two states, with either predominant CO or O coverage. Upon variation of one of the partial pressures, for example, a more or less abrupt transition between these states occurs, whereby the system may also show pronounced hysteresis effects—it exhibits bistability. Figure 2 reproduces corresponding experimental data for Pt(110), where the stationary work function change A4> (oxygen coverage) is plotted as a function of pco at fixed p0, and for various temperatures (24). Kinetic oscillations are ob-... 

A lattice-gas model of the NO + CO/Pt(l 00) reaction was found by Makeev and Kevrekidis (2004) to exhibit bistability and kinetic oscillations. In this simulation, the catalyst surface was represented by a square lattice with periodic boundary conditions. The model includes both chemical reactions and transitions of adsorbed reactants from the nearest-neighbor sites, which are in the... 

Autocatalysis is a distinctive phenomenon while in ordinary catalysis the catalyst re-appears from the reaction apparently untouched, additional amounts of catalyst are actively produced in an autocatalytic cycle. As atoms are not interconverted during chemical reactions, this requires (all) the (elementary or otherwise essential) components of autocatalysts to be extracted from some external reservoir. After all this matter was extracted, some share of it is not introduced in and released as a product but rather retained, thereafter supporting and speeding up the reaction(s) steadily as amounts and possibly also concentrations of autocatalysts increase. At first glance, such a system may appear doomed to undergo runaway dynamics ( explosion ), but, apart from the limited speeds and rates of autocatalyst resupply from the environment there are also other mechanisms which usually limit kinetics even though non-linear behavior (bistability, oscillations) may not be precluded ... 

Reaction fronts and oscillations The kinetic behavior of the model depends strongly on temperature, as shown in Figure 2. Below 350 K, AB production is zero, because the full coverage of one of the species blocks the grid. Under these circumstances, our simulated system represents a bistable medium. The two stable states cire poisoned states, in which either Aads or Bads blocks all surface sites. Strictly speaking, complete A-poisoning cannot occur because of A des-... 

In general, the concepts of bistability and hysteresis are related not only to the reaction kinetics but also to the time scale of the experiment. For this reason, the lattice size corresponding to the boundary between small and large lattices depends on the time scale of the experiment as well. MC simulations [66] indicate that often the boundary size is about 5x5. For somewhat larger lattices, one can observe the fluctuation-driven transitions between the high- and low-reactive regimes [42]. 

B. Borderie, D. Lavabre, G. Levy, J. C. Micheau, and J. P. Laplante, The bistable TP1D/CHC13 photoreaction Numerical simulation and experimental results, Int. J. Chem. Kinet. 24, 309-317... 

Fig. 4.35. Particle size-dependent bistability and hysteresis. On model system I (500-nm EBL-fabricated particles), the CO oxidation shows a perfectly stable bistability behavior. On the time scale accessible by the experiment (>10 s), we can arbitrarily switch between the two states by pulsing either pure CO or O2 (a and d). For the model system II (6-nm particles), a very slow transition toward a single global state is observed in the transition region between the CO- and O-rich reaction regimes (b and e). This behavior is assigned to fluctuation-induced transitions, which are accelerated by the presence of defect sites. For the smallest particles of the model system III (1.8 nm), a globally monostable kinetics is rapidly established under all conditions (c and f). For all experiments, the total flux of CO and O2 beams at the sample position was equivalent to a local pressure of 10" Pa. The surface temperature in (a-c) was 400 K and in (d-f) 415 K (from [147])...

Fig. 1.2. Depending on the parameters the FHN can either exhibit excitable (upper row), oscillatory (middle row) or bistable (lower row) kinetics, e = 0.05.

On the basis of this molecular level picture, Rebitsky et al. constructed a corrqrlete kinetic model of the remote control effect in selective oxidation, including transient effects (32). This predicts isothermal bistability in certain conditions. Such bistabilities have been found experimentally in a special reaction (33). For a catalyst of composition (by weight) Rm = acceptor/(acceptor+donor), the model gives the fraction a of Ae potentid sites which are redly active as a function of the reaction conditions (hydrocarbon and oxygen pressures, pnc and P02 respectively, temperature T and time t). 

A different kind of computing device is a parallel machine that can also be implemented by means of macroscopic chemical kinetics. For this purpose we choose a bistable chemical reaction, the iodate-arsenous acid reaction ... 

Model topology, that is, the interconnections between various components in the model as a whole, and the kinetic parameters associated with each connection determine the dynamies of the model. Interactions between components in the model can be either stimulatory or inhibitory. Series of interactions arranged in the form of loops can function as either positive or negative feedback. These feedback loops, depending on the parameter values, can display nonlinear dynamic behaviors such as oscillation and bistability (Bhalla etal., 2002 Hoffmann etal., 2002). These various features ean in turn modulate the response of the system to input signals, making complex dose responses such as switchlike or nonmonotonic ones possible. 

Many studies ctf the dynamics of bistable systems have been carried out, with particular attention paid to the relaxation kinetics near the transition... 

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