# Persistence

From Mathematics of Reaction Networks

A chemical reaction network endowed with some kinetic scheme is said to be **persistent** if initial present species are not allowed to approach extinction, either directly or asymptotically (i.e. as a limit of subsequences). That is to say, a network is persistent if for implies

for . For systems which are known to have bounded trajectories, this is equivalent to the condition where is the omega-limit set of the trajectory with initial condition .