# Persistence

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 $c_i(0) > 0$ for $i = 1, \ldots, m$ implies
$\liminf_{t > 0} c_i(t) > 0$
for $i = 1, \ldots, m$. For systems which are known to have bounded trajectories, this is equivalent to the condition $\omega(\vec{c}(0)) \cap \partial \mathbb{R}_{\geq 0}^n = \emptyset$ where $\omega(\vec{c}(0))$ is the omega-limit set of the trajectory with initial condition $\vec{c}(0)$.