论文标题
动态系统的弱可逆和缺陷零实现的独特性
Uniqueness of weakly reversible and deficiency zero realizations of dynamical systems
论文作者
论文摘要
根据质量行动动力学定律，反应网络以及速率常数的选择会唯一产生微分方程的系统。另一方面，不同的网络可以在质量行动动力学下生成相同的动态系统。因此，一般而言，识别动态系统的“基础网络”的问题通常不是很好。在这里，我们表明，识别潜在的弱可逆缺陷零网络的问题是良好的，因为该解决方案在存在时是唯一的。这在应用程序中可能非常有用，因为从动态和网络结构的角度来看，弱的缺陷零（$ \ textit {wr} _ \ textit {0} $）实现是最简单的。此外，尽管质量成分系统几乎可以表现出任何动力学行为，包括多稳定性，振荡和混乱，但$ WR_0 $系统对于任何速率常数选择都非常稳定：它们在每个不变多面体中具有独特的正稳态，并且无法引起振荡或混乱的动力学。我们还证明，对于唯一性，我们的两个假设（即弱的可逆性和零）都是必要的。
A reaction network together with a choice of rate constants uniquely gives rise to a system of differential equations, according to the law of mass-action kinetics. On the other hand, different networks can generate the same dynamical system under mass-action kinetics. Therefore, the problem of identifying "the" underlying network of a dynamical system is not well-posed, in general. Here we show that the problem of identifying an underlying weakly reversible deficiency zero network is well-posed, in the sense that the solution is unique whenever it exists. This can be very useful in applications because from the perspective of both dynamics and network structure, a weakly reversibly deficiency zero ($\textit{WR}_\textit{0}$) realization is the simplest possible one. Moreover, while mass-action systems can exhibit practically any dynamical behavior, including multistability, oscillations, and chaos, $WR_0$ systems are remarkably stable for any choice of rate constants: they have a unique positive steady state within each invariant polyhedron, and cannot give rise to oscillations or chaotic dynamics. We also prove that both of our hypotheses (i.e., weak reversibility and deficiency zero) are necessary for uniqueness.
