Chemical oscillator Brusselator

Brusselator) The Brusselator is a simple model of a hypothetical chemical oscillator, named after the home of the scientists who proposed it. (This is a common joke played by the chemical oscillator community there is also the Oregonator, Palo Altonator, etc.) In dimensionless form, its kinetics are... 

It means that one component is perturbed by amplitude a, a cosinusoidal forcing term with frequency co and phase (p. Recently particular attention has been paid to the response of nonlinear chemical oscillators that are periodically perturbed. The celebrated Brusselator model... 

As it was mentioned in Section 2.1.1, the concentration oscillations could be simulated quite well by a set of even two ordinary differential equations of the first order but paying the price of giving up the rigid condition imposed on interpretation of mechanisms of chemical reactions namely that they are based on mono- and bimolecular stages only (remember the Hanusse theorem [19]) An example of what Smoes [7] called the heuristic-topological model is the well-known Brusselator [2], Its scheme was discussed in Section 2.1.1 see equations (2.1.33) to (2.1.35). 

Gray, B. F. and Morley-Buchanan, T., 1985, Some criticism concerning the Brusselator model of an oscillating chemical reaction. J. Chem. Soc. Faraday Trans. 2 81, 77. 

Some autocatalytic chemical reactions such as the Brusselator and the Belousov-Zhabotinsky reaction schemes can produce temporal oscillations in a stirred homogeneous solution. In the presence of even a small initial concentration inhomogeneity, autocatalytic processes can couple with diffusion to produce organized systems in time and space. 

Another model of oscillating chemical reactions, the so-called Brusselator model was proposed by I. Prigogine and his collaborators at the Free University of Brussels. 

We consider first an abstract chemical model invented by a group of investigators in Brussels that has played an important role in the development of nonlinear dynamics. Because of its city of origin, it has become known as the Brusselator, or oscillator from Brussels. The chemical mechanism associated with this abstract model is ... 

By analysis and numerical simulation, Prigogine and Lefever demonstrated that their model shows homogeneous oscillations and propagating waves like those seen in the BZ system. The Brusselator was extremely important because it showed that a chemically reasonable mechanism could exhibit self-organization. 

In Chapter 1, we introduced the Brusselator model as the first chemical model to demonstrate oscillations and traveling waves. We will now analyze the Brusselator to illustrate how one might use the techniques that we have discussed to establish the behavior of a two-dimensional system. We recall that the equations are ... 

As a direct consequence of the particular role of Dynamics, as such,in the study of non-equilibrium behaviour of chemical systems, two classes of models are to be considered, depending on which aspect one is insisting on. Formal models, of mathematical or chemical-like nature, are designed to exhibit specific dynamical behaviours, without too much concern about chemical significance. Their aim is to provide examples of evolution equations of chemical reacting systems, as described by mass action kinetics, that are able to produce those exotic behaviours, such as bistability or multistability, between various types of attractors, like steady states, oscillations or deterministic chaos. A typical historical model of that kind is the "Brusselator ... 

Edens reports that, in the late 1960s, Prigogine shifted the center of his attention away from systems near equilibrium to those that are far from equilibrium — for those high-afSnity systems, entropy production was identified as the source of novel order. This shift in emphasis coincided with the development of widespread interest in instabilities and oscillations in chemical systems. The theoretical work of the Prigogine group, particularly investigations connected with the abstract chemical reaction-network model called the Brusselator, was centrally important... 

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