论文标题
Lyapunov函数PDES方法达到某些化学反应网络的稳定性
Lyapunov Function PDEs Method to the Stability of Some Chemical Reaction Networks
论文作者
论文摘要
本文有助于扩展Lyapunov函数PDE的有效性（Fang and Gao在[Siam and Gao In-In [Siam杂志上的应用动力学系统期刊》中，18（2019），第1163-1199页，第1163-1199页]，其解决方案被认为可以在稳定性分析质量化化学反应中以lyapunov的函数表现为Lyapunov函数）。通过定义一个称为复杂平衡生产的网络的新的网络，我们证明了Lyapunov函数PDES方法正在验证该类别网络的渐近稳定性，并根据物种以及任何两个特性依赖性的网络（如果包括某些温和的条件）与任何两种特征的自动启动性网络有关。一个值得注意的一点是，网络类别的类别是不可逆的，任何维度和任何缺陷的。我们将结果应用于一些实用的生化反应网络，包括出生死亡过程，基序相关的网络等，以说明有效性。
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.
