论文标题
具有零一个化学计量系数的反应网络的HOPF分叉
Hopf Bifurcations of Reaction Networks with Zero-One Stoichiometric Coefficients
论文作者
论文摘要
对于具有零一个化学计量系数的反应网络（或仅仅是零一个网络），我们证明，如果网络允许HOPF分叉，那么Stoichiometric矩阵的等级至少为四个。作为推论，我们表明，如果一个零一个网络接纳了HOPF分叉，那么它至少包含四个物种和五个反应。作为应用程序，我们表明存在在两个具有生物学意义的网络中的四四个子网络，具有HOPF分叉/振荡的能力：MAPK级联和ERK网络。我们提供了一个计算工具，用于计算具有HOPF分叉能力的所有四个物种，五反反应的网络。
For the reaction networks with zero-one stoichiometric coefficients (or simply zero-one networks), we prove that if a network admits a Hopf bifurcation, then the rank of the stoichiometric matrix is at least four. As a corollary, we show that if a zero-one network admits a Hopf bifurcation, then it contains at least four species and five reactions. As applications, we show that there exist rank-four subnetworks, which have the capacity for Hopf bifurcations/oscillations, in two biologically significant networks: the MAPK cascades and the ERK network. We provide a computational tool for computing all four-species, five-reaction, zero-one networks that have the capacity for Hopf bifurcations.
