Nicolis and Prigogine

In 1981 Nicolis and Prigogine [33] considered the behavior of far-from-equilibrium racemic mixtures that can bifurcate randomly into a direction of an enantiomeric singularity on passing through a critical point. They showed that such systems are profoundly sensitive to environmental asymmetries that at the critical point can cause the system to adopt one handedness over the other. 

Irregular behaviour of concentrations and the correlation functions observed in the chaotic regime differ greatly from those predicted by law of mass action (Section 2.1.1). Following Nicolis and Prigogine [2], the stochastic Lotka-Volterra model discussed in this Section, could be considered as an example of generalized turbulence. 

The components A (V represent the stationary and spatially uniform solution. These relations are associated with certain restrictions, such as T > 0 and c > 0 detailed balance is achieved, and hence physical systems are highly unique (Nicolis and Prigogine, 1989). 

Stability depends on whether the perturbation x grows or decays with time. A perturbation may be due to the interference of the environment with the intrinsic dynamics of the system or intrinsic internal deviations called fluctuations that the system generates spontaneously. The property of stability refers to several responses of systems to various types of perturbations (Nicolis and Prigogine, 1989) ... 

Nicolis and Prigogine (1989) have produced an excellent introduction, and the understanding of complexity theory promises to have a major impact on ecology and environmental toxicology. 

Systems can be classified on different basis. The most fundamental of which is that based on thermodynamic principles and on this basis they can be classified into (Prigogine el ai, 1973 Nicolis and Prigogine, 1977) ... 

There are a number of excellent treatments of the Turing instability. A classic and comprehensive account can be found in the book by Murray,which includes fascinating treatments of pattern formation in animal-shaped domains (to address the question of animal coat patterns ). A less advanced but highly recommended presentation can be found in the book by Edelstein-Keshet, which contains a wealth of information on mathematical treatments of biological systems. The following description is adapted from Ref. 34, which draws on both of these sources. For more advanced discussions, the reader may wish to consult the thermodynamics oriented treatment of Nicolis and Prigogine. ... 

In 1977, Nicolis and Prigogine summarized the work of the Brussels school in a book entitled Self-Organization in Nonequilihrium Systems. For his contributions to the study of nonequilibrium systems, Ilya Prigogine was awarded the 1977 Nobel prize in chemistry. 

Domain II represents an area in which the steady-state solution is unstable and where fluctuations increase monotonically. In domain III, the steady-state solution is also unstable here, however, fluctuations are amplified and undergo oscillations. Taken with kind permission from Nicolis and Prigogine (1977), Self-Organization in Nonequilibrium Systems, p. 133, John Wiley and Sons. 

A detailed theoretical analysis of the Brusselator has been presented recently in a monograph by Nicolis and Prigogine (17). Relevant aspects of this development are reviewed in the following paragraphs ... 

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