Macroscopic Description of Complex Self-Organizing System: Belousov–Zhabotinsky Reaction

Based on the information theory of mutifractal objects was developed the method for analysis of complex self-organized system, such as living cells. To demonstrate some of the features of the analysis we choose the simplest system—the Belousov–Zhabotinsky reaction (chemical clock). It is always composed of observed sequence of states stable for certain period of time and the experimenter has full control of mechanical constraints imposed on the system. We use the Renyi information entropy equation for calculation of information gain by which a point contributes to the total information in the image. In this way we create characteristic vector of the system state in phenomenological coordinates of phase space. We have also derived related variables, the point information gain entropy and point information gain entropy density. The later values are unique to structured information. The ultimate goal of the method is to determine the characteristics of a system which best characterize momentary multifractal properties of the system. The relation between the phenomenological phase space and the internal coordinates of the system remain unknown.