论文标题
一种用于查找多项式动态系统的弱可逆缺陷零实现的算法
An algorithm for finding weakly reversible deficiency zero realizations of polynomial dynamical systems
论文作者
论文摘要
具有多项式右侧的微分方程系统在应用中非常普遍。另一方面，由于复杂动力学的可能性：吸引力的多个盆地，振荡甚至混乱的动力学，它们的数学分析通常非常具有挑战性。即使我们将注意力限制在质量行动系统上，所有这些复杂的动力学行为仍然是可能的。另一方面，如果多项式动力学系统具有弱可逆的零（$ wr_0 $）实现，则已知其动力学非常简单：振荡和混乱的动力学已被禁止，直到线性保护法律，并且有一个单一的积极稳定状态，即渐近稳定的稳定状态。在这里，我们描述了一种用于查找$ WR_0 $实现多项式动态系统的算法。
Systems of differential equations with polynomial right-hand sides are very common in applications. On the other hand, their mathematical analysis is very challenging in general, due to the possibility of complex dynamics: multiple basins of attraction, oscillations, and even chaotic dynamics. Even if we restrict our attention to mass-action systems, all of these complex dynamical behaviours are still possible. On the other hand, if a polynomial dynamical system has a weakly reversible deficiency zero ($WR_0$) realization, then its dynamics is known to be remarkably simple: oscillations and chaotic dynamics are ruled out and, up to linear conservation laws, there exists a single positive steady state, which is asymptotically stable. Here we describe an algorithm for finding $WR_0$ realizations of polynomial dynamical systems, whenever such realizations exist.
