A Robust Lyapunov Criterion for Nonoscillatory Behaviors in Biological Interaction Networks

We introduce the notion of nonoscillation, propose a constructive method for its robust verification, and study application to biological interaction networks (also known as, chemical reaction networks). begin by revisiting Muldowney’s result on nonexistence periodic solutions based variational system second additive compound Jacobian nonlinear system. show that exponential stability latter rules out limit cycles, quasi-periodic solutions, broad classes oscillatory behavior. focus then equations arising in with general kinetics, we dynamics aforementioned can be embedded linear differential inclusion. algorithms constructing piecewise Lyapunov functions certify global nonoscillatory Finally, apply our techniques several regulated enzymatic where available methods are not able provide any information about their qualitative