PERSISTENCE AND PERMANENCE OF MASS-ACTION AND POWER-LAW DYNAMICAL SYSTEMS
PERSISTENCE AND PERMANENCE OF MASS-ACTION AND POWER-LAW DYNAMICAL SYSTEMS
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DOI：
10.1137/100812355
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发表时间：
2013-01-01
影响因子：
1.9
通讯作者：
Pantea, Casian
中科院分区：
文献类型：
--
作者：
Craciun, Gheorghe;Nazarov, Fedor;Pantea, Casian
持久性和持久性是描述解的长期行为的动力系统的性质，特别是指定正解是否接近正正交点的边界。质量作用系统（或更一般的幂律系统）在化学、生物学和工程学中非常常见，经常被用来描述相互作用网络中的动力学。证明了对于任意的反应速率参数，由弱可逆网络导出的两种群质量作用系统都是持久的和永久的。此外，我们证明了一个更大的类的网络，称为endotractic网络，也会产生永久的系统，即使反应速率参数随时间变化（允许外部信号的影响）。这些结果也适用于幂律系统和其他非线性动力系统。此外，这些结果背后的思想使我们能够证明三种群系统的全局吸引子猜想。
Persistence and permanence are properties of dynamical systems that describe the long-term behavior of the solutions and in particular specify whether positive solutions approach the boundary of the positive orthant. Mass-action systems (or more generally power-law systems) are very common in chemistry, biology, and engineering and are often used to describe the dynamics in interaction networks. We prove that two-species mass-action systems derived from weakly reversible networks are both persistent and permanent, for any values of the reaction rate parameters. Moreover, we prove that a larger class of networks, called endotactic networks, also give rise to permanent systems, even if the reaction rate parameters vary in time (to allow for the influence of external signals). These results also apply to power-law systems and other nonlinear dynamical systems. In addition, ideas behind these results allow us to prove the global attractor conjecture for three-species systems.