Piecewise Linear in Rates Lyapunov Functions for Complex Reaction Networks

Piecewise-Linear in Rates (PWLR) Lyapunov functions are introduced for a class of Complex 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 guarantee their asymptotic stability with respect to the corresponding stoichiometric compatibility class. We give the definition of these Lyapunov functions, present their basic properties, and provide algorithms for constructing them. Examples are provided, relationship with consensus dynamics are discussed, and future directions are elaborated.