Bistability and oscillations

Interestingly, the simple model is already sufficient to exhibit a variety of dynamic regimes, including bistability and oscillations. 

Hendiiksen BLM, Bobaru SC, Frenken JWM (2005). Bistability and oscillations in CO oxidation studied with scanning tunnelhng microscopy inside a reactor. Catal Today, 105, 234... 

Oscillators, Part 5. Bistability and Oscillations in the Autocatalytic Chlorite-Iodide Reaction in a Stirred-Flow Reactor, J. Am. Chem. Soc. 104(2) 504-509... 

Mota A, Gonzalez ER, Eiswirth M (2013). Continuous CO electroxidation bistability and oscillations. Phys Chem Chem Phys (to Submitted)... 

The systems discussed above belong to the class of non-linear dynamical systems. In such cases, the non-linear equation represents evolution of a solution with time or some variable like time. Such non-linear equations may be (i) algebraic, (ii) functional, (iii) ordinary partial differential equations and (iv) integral equations or a combination of these. Non-equilibrium systems can be defined by the type of equations as defined above involving the bifurcation parameter. The solution may change depending on the particular values of parameter. The solutions change at bifurcation points. Such situations do occur in the form of bistability and oscillations. 

We discuss below a few representative systems where (i) only bistability occurs and (ii) both bistability and oscillations occur. Bistability results for some typical chemical systems are discussed below. Quite a few different cases [6, 7] have earlier been discussed by Field and Burger [8]. 

Pacault et al. [15] studied this oscillatory reaction in a CSTR and reported complex oscillations, multiple steady states accompanied by a variety of bifurcation and hysteresis phenomena. They proposed a mechanism which was subjected to computer simulation. The [I03]o — [l2]o clearly demonstrates two separate regions of bistability and oscillations. Noyes et al. [16] and Furrow et al. [17] suggested same mechanism independently by using different methods, thereby supporting both the validity of the mechanism and their approach... 

Since electro-kinetic systems can be maintained in the far-from-equilibrium region to any desired extent by controlling the variables, they constitute a very good system for the study of dynamic instability from experimental angle. A brief discussion of bistability and oscillations in electro-kinetic phenomena from an experimental point of view is given below. 

Using these assumptions, it has been shown [6, 13] that van der Pol type equation can be deduced. Theoretical formulations of Teorell as well as that of Kobatake and Fujita have been compared, and it has been shown [13-15] that both involve certain assumptions but both yield van der Pol type equation. It also turns out that there is no relationship between bistability and oscillations. The validity of the two-variable model has been further examined by comparing the experimental results with computer simulation based on the use of experimentally determined parameters [14], which did not yield satisfactory results. 

In the non-linear region, exotic non-equilibrium phenomena such as bifurcation from steady state to bistability and oscillations (in time and space) are observed. New mathematical methodology based on non-linear dynamics has been evolved for investigating such phenomena as discussed in Chapter 8. The essential point to note is that such complex phenomena arise when more than three forces are evolved in addition to the occurrence of multi-process as discussed in Parts Two and Three. Bifurcation process... 

In batch conditions, the model behaves (as does the experimental system) as a clock reaction, with an induction period followed by a sudden jump of several orders of magnitude in H and then an exponential decrease in H. Under flow conditions, bistability and oscillations are obtained. The model can easily be adapted to describe a wide variety of pH oscillators, including iodate-sulfite-thiourea (Rabai et ah, 1987), iodate-sulfite-thiosulfate (Rabai and Beck, 1988), periodate-thiosulfate (Rabai et ah, 1989a), periodate-hydroxylamine (Rabai and Epstein, 1989), and iodate-hydroxylamine (Rabai and Epstein, 1990). 

Bistability and Oscillations in a Flow Reactor The Systems H2O2-KI with and... 

Figure 5- Bistability and oscillation in a typical chemical system (see text), a) Simple bistability b) Effect (- -) of adding a feedback species c) Behavior of the system in b) as function of time d) Cross-shaped phase diagram.

No kinetic oscillations, rather just bistability, could be detected with the Pt(l 11) surface, whereas the other orientations of the crystal showed bistability and oscillations [8]. The reason for this is that the lifting of the reconstruction enhances the oxygen sticking coefficient. Consequently, oscillatory behavior occurs when the partial pressures pco and po are adjusted in such a way that the CO adsorption rate is faster (slower) than the O2 uptake on the reconstructed (1x1) surface. The reconstructed surface will take up CO and the 1 X 1 will form, which adsorbs oxygen faster, which, in turn, reduces the CO coverage by reactive removal. (Note that CO adsorption is not noticeably structure sensitive.)... 

The model exhibits bistability and oscillations in a wide range of parameters. It is worthwhile to note, however, that the amplitude of oscillations (Fig. 3a inset) exceeds those obtained in the full model (not shown). The presence of carbon dioxide and its derivatives reduces the range of oscillations to about pH 4-6 with negligible effect on the frequency, hence pH indicators for monitoring oscillations... 

C. E. Dateo, M. Orban, P. De Kepper, and I. R. Epstein, Systematic design of chemical oscillators. 5. Bistability and oscillations in the autocatalytic chlorite-iodide reaction in a stirred-flow reactor, Journal of the American Chemical Society, vol. 104, no. 2, pp. 504-509, 1982. 

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