SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 1-37, January 2021.
Deciding whether and where a system of parametrized ordinary differential equations displays bistability, that is, has at least two asymptotically stable steady states for some choice of parameters, is a hard problem. For systems modeling biochemical reaction networks, we introduce a procedure to determine, exclusively via symbolic computations, the stability of the steady states for unspecified parameter values. In particular, our approach fully determines the stability type of all steady states of a broad class of networks. To this end, we combine the Hurwitz criterion, reduction of the steady state equations to one univariate equation, and structural reductions of the reaction network. Using our method, we prove that bistability occurs in open regions in parameter space for many relevant motifs in cell signaling.

中文翻译：

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反应网络中双稳态的符号证明

SIAM应用动力系统杂志，第20卷，第1期，第1-37页，2021年1月。
很难确定参数化的常微分方程组的系统是否以及在何处显示双稳态，也就是说，对于某些参数选择，至少具有两个渐近稳定稳态。对于为生化反应网络建模的系统，我们引入了一种程序，专门通过符号计算来确定未指定参数值的稳态稳定性。特别是，我们的方法完全确定了广泛网络类别的所有稳态的稳定性类型。为此，我们结合了Hurwitz准则，将稳态方程简化为一个单变量方程以及将反应网络进行结构简化的方法。使用我们的方法，我们证明了双稳态发生在参数空间中细胞信号传导中许多相关基序的开放区域中。