Narrow Results

In this paper we revisit a switching circuit designed by the authors and present a theoretical analysis on the existence of chaos in this circuit. For the ordinary differential equations describing this circuit, we give a computer-aided proof in terms of cross-section and Poincare map, by applying a modern theory of topological horseshoes theory to the obtained Poincare map, that this map is semiconjugate to the two-shift map. This implies that the corresponding differential equations exhibit chaos.

In this paper we present in a tutorial fashion the framework of reaction systems — a formal approach to investigating processes instigated by the living cell. The main idea behind this approach is that this functioning is determined by interactions between biochemical reactions, and these interactions are based on two mechanisms, facilitation and inhibition.