Lyapunov Function PDEs to the Stability of Some Complex Balancing Derivative and Compound Networks
(2022) IEEE Transactions on Automatic Control — Vol. 67, n° 10, p. 5026-5038 (2022)
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- Abstract
- This paper contributes to extending the validity of Lyapunov function PDEs whose solution is conjectured to be able to behave as a Lyapunov function in stability analysis to more mass-action chemical reaction networks. First, we have proved that the Lyapunov function PDEs method is valid in capturing the asymptotic stability of the networks compounded of a complex balanced network and any species-dependent twospecies autocatalytic network if some moderate conditions are included. Then by defining a new class of networks, called complex balanced produced networks, we also show the asymptotic stability of this class of networks, and also to their compound with any species-independent 1-dimensional network and with any species-dependent two-species autocatalytic network under some conditions by using the same method. A notable point is that these classes of networks are non-weakly reversible, of any dimension, and of any deficiency. Finally, we apply our results to some practical biochemical reaction networks including birthdeath processes, motifs related networks etc., to illustrate validity.
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Citations
Yafei Lu, Chuanhou Gao, & Denis Dochain. (2022). Lyapunov Function PDEs to the Stability of Some Complex Balancing Derivative and Compound Networks. IEEE Transactions on Automatic Control, 67(10), 5026-5038. https://doi.org/10.1109/TAC.2021.3115889 (Original work published 2022)