On the relation between w-limit set and boundaries of mass-action chemical reaction networks

omega-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 w-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 w-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 w-limit points. Further, we derive the w-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.(c) 2022 Elsevier Ltd. All rights reserved.