The choice of the state space representation of a system can turn into a prominent advantage or burden in any endeavour to mathematically model dynamical systems since it entails the analytical tractability of the related modelling formalism and the efficiency of the numerical computation. The Reaction-Based Model (RBM) of the state space, which is presented in this article, is a novel formalization of the kinetics of a system of interacting molecules. According to our representation, the state Sμ of a system of M reactions and N molecular species, is identified with the occurrence of the reaction Rμ(μ = 1, …, M). The transition between any two states Sμ and Sν is modelled as a first-order reaction Sμ→ Sν and described by mass action-like equation for the time derivative of the variables P(Sμt) and P(Sν; t), which denote the probabilities that the system lies in the two states respectively. The rate equations for the state probabilities are coupled with those for the abundance of molecular species. The rate equations along with the initial conditions define the Cauchy problem whose solution describes the system's dynamics. The RBM has been successfully applied to a severely stiff biological case study.The numerical solutions of the system's dynamics turned out to be computationally more efficient and in agreement with the results of the stochastic and hybrid stochastic/deterministic simulation algorithms.

中文翻译：

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基于反应的化学反应系统状态空间模型可以进行高效的仿真。

选择系统的状态空间表示形式可能会成为任何对数学建模动力学系统的努力的显着优势或负担，因为这需要相关建模形式的分析可处理性以及数值计算的效率。本文介绍的基于状态空间的基于反应的模型（RBM）是相互作用分子系统动力学的新颖形式化形式。根据我们的表示，由反应Rμ（μ= 1，…，M）的发生确定了M个反应和N个分子种类的系统的状态Sμ。任意状态Sμ和Sν之间的跃迁被建模为一阶反应Sμ→Sν，并通过类似于质量作用的方程式来描述变量P（Sμt）和P（Sν; t）的时间导数，分别表示系统处于两种状态的概率。状态概率的速率方程与分子种类丰富的速率方程耦合。速率方程式和初始条件一起定义了柯西问题，该问题的解决方案描述了系统的动力学特性。RBM已成功应用于严重僵化的生物学案例研究。系统动力学的数值解决方案在计算上更加有效，并且与随机和混合随机/确定性仿真算法的结果相符。速率方程式和初始条件一起定义了柯西问题，该问题的解决方案描述了系统的动力学特性。RBM已成功应用于严重僵化的生物学案例研究。系统动力学的数值解决方案在计算上更加有效，并且与随机和混合随机/确定性仿真算法的结果相符。速率方程式和初始条件一起定义了柯西问题，该问题的解决方案描述了系统的动力学特性。RBM已成功应用于严重僵化的生物学案例研究。系统动力学的数值解决方案在计算上更加有效，并且与随机和混合随机/确定性仿真算法的结果相符。