Capturing persistence of high-dimensional delayed complex balanced chemical reaction systems via decomposition of semilocking sets

With the increasing complexity of time-delayed systems, the diversification of boundary types of chemical reaction systems poses a challenge for persistence analysis. This paper focuses on delayed complex balanced mass-action systems (DeCBMAS) and it derives that some boundaries of a DeCBMAS cannot contain an.-limit point of some trajectory with positive initial conditions by using the method of semilocking set decomposition and the property of the facet, further expanding the range of persistence of DeCBMASs. These findings demonstrate the effectiveness of semilocking set decomposition to address the complex boundaries and offer insights into the persistence analysis.