论文标题
在广义质量成分系统中复杂平衡平衡的线性稳定性的足够条件
Sufficient conditions for linear stability of complex-balanced equilibria in generalized mass-action systems
论文作者
论文摘要
通用的质量表演系统是由化学反应网络引起的幂律动力学系统。从本质上讲，化学和生物学中使用的每个非负ODE模型（例如，在生态学和流行病学中），甚至在经济学和工程学中都可以以这种形式编写。先前的结果集中在所有速率常数的特殊稳态（复杂平衡平衡）的存在上，从而排除了多个（特殊）稳态。最近，已经获得了线性稳定性的必要条件。 在这项工作中，我们为所有速率常数（以及其他稳态的不存在）提供了足够的条件。特别是，通过签名矢量条件（在化学计量系数和动力学订单上），我们保证Jacobian矩阵为$ p $ -matrix。从技术上讲，我们使用图形拉普拉斯式的新分解，该分解允许考虑（广义）单项。或者，我们使用循环分解，该分解允许所有雅各布矩阵的线性参数化。无论如何，我们保证稳定性而无需明确计算稳态。我们在化学和生物学的示例中说明了我们的结果：广义Lotka-Volterra系统和SIR模型，两个组件信号系统，以及酶促的徒劳循环。
Generalized mass-action systems are power-law dynamical systems arising from chemical reaction networks. Essentially, every nonnegative ODE model used in chemistry and biology (for example, in ecology and epidemiology) and even in economics and engineering can be written in this form. Previous results have focused on existence and uniqueness of special steady states (complex-balanced equilibria) for all rate constants, thereby ruling out multiple (special) steady states. Recently, necessary conditions for linear stability have been obtained. In this work, we provide sufficient conditions for the linear stability of complex-balanced equilibria for all rate constants (and also for the non-existence of other steady states). In particular, via sign-vector conditions (on the stoichiometric coefficients and kinetic orders), we guarantee that the Jacobian matrix is a $P$-matrix. Technically, we use a new decomposition of the graph Laplacian which allows to consider orders of (generalized) monomials. Alternatively, we use cycle decomposition which allows a linear parametrization of all Jacobian matrices. In any case, we guarantee stability without explicit computation of steady states. We illustrate our results in examples from chemistry and biology: generalized Lotka-Volterra systems and SIR models, a two-component signaling system, and an enzymatic futile cycle.
