Persistence Results for Chemical Reaction Networks with Time-Dependent Kinetics and No Global Conservation Laws

New checkable criteria for persistence of chemical reaction networks are proposed, which extend and complement existing ones. The new results allow the consideration of reaction rates which are time-varying, thus incorporating the effects of external signals, and also relax the assumption of existence of global conservation laws, thus allowing for inflows (production) and outflows (degradation). For time-invariant networks, parameter-dependent conditions for persistence of certain classes of networks are provided. As an illustration, two networks arising in the systems biology literature are analyzed, namely a hypoxia network and an apoptosis network.

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