Out-of-equilibrium self-organization

This notion of bifurcation point, connected with those of instability and fluctuations, is the basis of this branch of science of self-organization in out-of-equilibrium systems. The story begins with Alan Turing, who, in search of the chemical basis of 

The next two important steps in this narrative are considered to be the following (i) the description of the bruxellator by Prigogine and Lefever, who, following on from Turing s work, analyzed theoretically the ingredients that should be present in a model of chemical reactions in order to produce spatial self-organization (Prigogine and Lefever, 1968) (ii) the description of the Belousov-Zhabotinsky (B-Z) reaction. 

However at a critical distance from equilibrium, the system must choose between two possible pathways, represented by the bifurcation point Ac. The continuation of the initial pathway, indicated by a broken hne, indicates the region of instability. The concentration of the species A and the value of A assume quite different values, and the more so, the further from equilibrium. An important point is that the choice between the two branching directions is casual, with 50 50 probability of either. The critical point Ac has particular importance because beyond it, the system can assume an organized structure. Here the term self-organization is introduced as a consequence of the dissipative structures, dissipative in the sense that it results from an exchange of matter and energy between system and environment (we are considering open systems). 

It is worthwhile also mentioning that the origin of homochirality has been viewed in terms of a bifurcation scenario (Kondepudi and Prigogine, 1981 Kondepudi et al, 1985). In this case, the homochirality present on Earth would be a product of contingency. 

These organized structures can take the form of oscillations, and this is indeed the case for the Zabotinski-Belousov (Z-B) reaction, observed in the 1950s by the Russian chemist Boris Belousov (see in Winfree, 1984). It is interesting to note 

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