Construction of the phenomenological model of Belousov–Zhabotinsky reaction state trajectory

Abstract

The Belousov–Zhabotinsky reaction is used as an example of a self-organizing system which is easily and intelligibly observable, and experimentally accessible. The analysis does not require elaborate reconstruction of series of three-dimensional images as in the case of bird flocks, fish schools or organ behaviour. The analysis of living cells microscopic image series is even more elaborate. Moreover, the experimenter in the case of the chemical clock has full control of the mechanical constraints imposed on the system. In this, contributions are reported using both experimental and theoretical results of the BZ reaction as an experimental tool for the analysis of behaviour of the self-organizing system. We have created a state trajectory using several selected image identifiers (point information gain entropy – H_α). The H_α values define an approximate state space which may be analysed using multivariate analysis. In this report we provide results of this analysis.

Keywords:

• information entropy
• state trajectory
• multifractal dimension
• multivariate analysis
• phase space

2010 AMS Subject Classifications:

• 97A17
• 62Hxx

Acknowledgements

This work was partly supported by projects CENAKVA (CZ.1.05/2.1.00/01.0024) and by the grant GAJU152//2010/Z of the Grant Agency of the University of South Bohemia. The authors thank Petr Cisar and Tomáš Náhlík for their extensive help in the experimental and theoretical aspects of the work described in the article.