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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 behaveas a Lyapunov function) in stability analysisto more mass-action chemicalreaction networks. By defining a new class of networks, called complexbalancedproduced networks, we have proved that the Lyapunov function PDEs method isvalidin capturing the asymptotic stability of this class of networks, and alsoto their compound withany 1-dimensional independent network according tospecies and with any two-species autocatalyticnon-independent network if somemoderate conditions are included. A notable point is that thesethree classes ofnetworks are non-weakly reversible, any dimensional and of any deficiency. Weapplyour results to some practical biochemical reaction networks includingbirth-death processes, motifsrelated networks etc., to illustrate validity.

Lyapunov Function PDEs Method to the Stability of Some Chemical Reaction Networks