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Evolution and Religious Creation MythsHow Scientists Respond$

Paul F. Lurquin and Linda Stone

Print publication date: 2007

Print ISBN-13: 9780195315387

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780195315387.001.0001

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(p.195) Appendix 1

(p.195) Appendix 1

The Brusselator

Source:
Evolution and Religious Creation Myths
Publisher:
Oxford University Press

The Brusselator is the first computer‐generated dissipative structure developed by Ilya Prigogine and colleagues at the University of Brussels, Belgium, in the early 1970s. It is based on hypothetical coupled chemical reactions, some of which are autocatalytic. These reactions involve four compounds, A, B, D, and E, and two intermediate compounds, X and Y, which do not accumulate in the reaction vessel because they are converted into E and D as the reactions progress. Compounds A and B are fed into the system in a continuous manner. The reactions are written

  • A → X

  • B + X → Y + D

  • 2X + Y → 3X

  • X → E

and can be graphed as follows:

Appendix 1The Brusselator

The two loops connecting compounds X and Y represent the autocatalytic portion of the reaction. Using conditions far from thermodynamic equilibrium, it can be shown that the distribution (concentration) of compound X in (p.196)

Appendix 1The Brusselator

Figure A.1 Cross section of a reaction vessel containing the Brusselator. The solid lines and arrows show the variations in the concentration of compound X as a function of space and time. The dotted line represents an invariant equilibrium situation.

(p.197)
Appendix 1The Brusselator

Figure A.2 The Brusselator reaction vessel seen from the top. Darker regions indicate a higher concentration of compound X. The arrows denote the directions of the concentration wave.

the reaction vessel fluctuates in time and space. In other words, the reaction mixture spontaneously acquires a spatial and temporal structure (order).

The fluctuation of the concentration of X as a function of space is shown in figure A.1 at six different time intervals. Initially, the concentration of X decreases in the center of the reaction vessel, followed by a wave (a moving ring) that eventually makes the concentration of X higher in the center of the vessel. The process then reverses itself, and a wave of concentration of X leaves the center to reach the border of the reaction vessel. These oscillations (p.198) continue indefinitely as long as reactants A and B are fed into the system. Figure A.2 shows the phenomenon seen from the top of the reaction vessel. The Brusselator is not just a theoretical model; it represents very well the structures seen in the actual Belousov‐Zhabotinsky reaction, a chemical reaction that displays moving, concentric rings of colored reactants (see appendix 2). Other dissipative structures show wavelike patterns in space that are stable in time. Such patterns are seen in developing embryos. The application of the mathematics of dissipative structures to living systems is still in its infancy and awaits multidisciplinary collaborations for potential fruition in the life sciences.