  In this paper, we develop a method to generate the Lyapunov function for
stability analysis for chemical reaction networks. Based on the Chemical Master
Equation, we derive the Lyapunov Function partial differential equations
(PDEs), whose solution approximates the scaling non-equilibrium potential and
serves as the candidate Lyapunov function for the given network. We further
prove that for any chemical reaction network the solution (if exists) of the
PDEs is dissipative. Moreover, the proposed method of Lyapunov Function PDEs is
qualified for analyzing the asymptotic stability of complex balanced networks,
all networks with $1$-dimensional stoichiometric subspace and some special
networks with more than $2$-dimensional stoichiometric subspace if some
moderate conditions are added. Several examples are presented to illustrate the
efficiency of the method.
