  This paper contributes to extending the validity of Lyapunov function PDEs
(in-vented by Fang and Gao in [SIAM Journal on Applied Dynamical Systems,
18(2019), pp. 1163-1199]and whose solution is conjectured to be able to behave
as a Lyapunov function) in stability analysisto more mass-action chemical
reaction networks. By defining a new class of networks, called complexbalanced
produced networks, we have proved that the Lyapunov function PDEs method is
validin capturing the asymptotic stability of this class of networks, and also
to their compound withany 1-dimensional independent network according to
species and with any two-species autocatalyticnon-independent network if some
moderate conditions are included. A notable point is that thesethree classes of
networks are non-weakly reversible, any dimensional and of any deficiency. We
applyour results to some practical biochemical reaction networks including
birth-death processes, motifsrelated networks etc., to illustrate validity.
