The steady-state degree of a chemical reaction network is the number of complex steady-states, which is a measure of the algebraic complexity of solving the steady-state system. In general, the steady-state degree may be difficult to compute. Here, we give an upper bound to the steady-state degree of a reaction network by utilizing the underlying polyhedral geometry associated with the corresponding polynomial system. We focus on three case studies of infinite families of networks, each generated by joining smaller networks to create larger ones. For each family, we give a formula for the steady-state degree and the mixed volume of the corresponding polynomial system.

化学反应网络的稳态度是复杂稳态的个数，是求解稳态系统代数复杂度的度量。通常，稳态度可能难以计算。在这里，我们通过利用与相应多项式系统相关的潜在多面体几何形状，给出了反应网络稳态度的上限。我们专注于无限网络家族的三个案例研究，每个案例研究都是通过加入较小的网络来创建较大的网络而产生的。对于每个族，我们给出了相应多项式系统的稳态度和混合体积的公式。