ABSTRACT
One of the most essential temporal structures in life systems is a cycle, which can be observed in any hierarchy of living things, such as TCA cycle in cytoplasmic level, the cell cycle in cell division, and the life cycle of living things. The importance of this structure has been pointed out by several authors, such as Eigen’s hypercycle, Maturana’s autopoiesis, Kauffman’s NK network, and Fontana’s Algorithmic Chemistry. However, these researches do not systematically address the conditions under which such cycle structures will emerge and become stable. In this paper, abstract rewriting system on a multiset is introduced to a model chemical reaction as a symbolic rewriting system acting on a multiset, which can be viewed as a chemical reaction system in a test tube. By use of this model, we made experiments on Brusselator model (the Brusselator is a model of chemical oscillations which are found on the Belousov-Zabotinsky reaction). And we confirm that non-linear oscillation emerges.
