On the relation between [formula omitted]-limit set and boundaries of mass-action chemical reaction networks

Abstract

ω-limit set can be used to understand the long term behavior of a dynamical system. In this paper, we use the Lyapunov Function PDEs method, developed in our previous work, to study the relation between ω-limit points and boundaries for chemical reaction networks equipped with mass-action kinetics. Using the solution of the PDEs, some new checkable criteria are proposed to diagnose non ω-limit points of the network system. These criteria are successfully applied to verify that non-semilocking boundary points and some semilocking boundary points are not ω-limit points. Further, we derive the ω-limit theorem that precludes the limit cycle of some biochemical network systems. The validity of the results are demonstrated through some abstract and practical examples of chemical reaction networks.