Journal ArticleDOI
Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction
TLDR
In this paper, the authors generalized the chemical mechanism of Field, Koros, and Noyes for the oscillatory Belousov reaction by a model composed of five steps involving three independent chemical intermediates.Abstract:
The chemical mechanism of Field, Koros, and Noyes for the oscillatory Belousov reaction has been generalized by a model composed of five steps involving three independent chemical intermediates. The behavior of the resulting differential equations has been examined numerically, and it has been shown that the system traces a stable closed trajectory in three dimensional phase space. The same trajectory is attained from other phase points and even from the point corresponding to steady state solution of the differential equations. The model appears to exhibit limit cycle behavior. By stiffly coupling the concentrations of two of the intermediates, the limit cycle model can be simplified to a system described by two independent variables; this coupled system is amenable to analysis by theoretical techniques already developed for such systems.read more
Citations
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Journal ArticleDOI
Evolutionary games on graphs
György Szabó,Gábor Fáth +1 more
TL;DR: The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
Journal ArticleDOI
DNA as a universal substrate for chemical kinetics
TL;DR: It is shown that systems of DNA molecules can be constructed that closely approximate the dynamic behavior of arbitrary systems of coupled chemical reactions, by using strand displacement reactions as a primitive, and systems implementing feedback digital logic and algorithmic behavior are illustrated.
Journal ArticleDOI
Mixed-Mode Oscillations with Multiple Time Scales
Mathieu Desroches,John Guckenheimer,Bernd Krauskopf,Christian Kuehn,Hinke M. Osinga,Martin Wechselberger +5 more
TL;DR: This survey of different types of MMOs is given, concentrating its analysis on MMOs whose small-amplitude oscillations are produced by a local, multiple-time-scale “mechanism.”
References
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Journal ArticleDOI
The Chemical Basis of Morphogenesis
TL;DR: In this article, it is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis.
Book
Thermodynamic Theory of Structure, Stability and Fluctuations
Paul Glansdorff,Ilya Prigogine +1 more
Journal ArticleDOI
Concentration wave propagation in two-dimensional liquid-phase self-oscillating system.
TL;DR: This work deals with patterns in a thin layer of solution, in which cerium ions catalyse the oxidation of analogues of malonic acid by bromate by oscillations in the solution colour.