New Approach to the Stability of Chemical Reaction Networks: Piecewise Linear in Rates Lyapunov Functions

Piecewise-linear in rates (PWLR) Lyapunov functions are introduced for a class of chemical reaction networks (CRNs). In addition to their simple structure, these functions are robust with respect to arbitrary monotone reaction rates, of which Mass-Action is a special case. The existence of such functions ensures the convergence of trajectories towards equilibria, and can be used to establish their asymptotic stability with respect to the corresponding stoichiometric compatibility class. We give the definition of these Lyapunov functions, prove their basic properties, and provide algorithms for constructing them. Examples are provided, relationship with consensus dynamics are discussed, and future directions are elaborated.