The flow topology of chemical reaction networks

Analysis of the flow topology of dynamic systems modelling chemical reaction networks leads to the following conclusions: (1) a connected chemical system with a negative feedback circuit containing all except one of the internal species (phase determining intermediates) can exhibit chaotic oscillations; (2) a chemical system in which the only negative feedback circuit contains all of the internal species can exhibit periodic oscillations; (3) a chemical system containing no negative feedback circuits cannot exhibit oscillatory behavior but only multiple steady states. In this analysis a negative feedback circuit refers to a circuit containing an odd number of inhibitory relationships between internal species.