Piecewise Linear in rates Lyapunov functions for Complex Reaction Networks
Piecewise Linear in rates Lyapunov functions for Complex Reaction Networks
复制标题
复杂反应网络的速率 Lyapunov 函数的分段线性
DOI：
10.1109/cdc.2013.6760606
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
D. Angeli
中科院分区：
文献类型：
--
作者：
M. A. Al;D. Angeli
针对一类复杂反应网络，引入了速率分段线性李雅普诺夫函数。除了它们简单的结构，这些功能是强大的任意单调的反应速率，其中质量作用是一个特殊的情况。这样的功能的存在，确保收敛的轨迹向平衡，并保证其渐近稳定性相对于相应的化学计量相容类。我们给出了这些李雅普诺夫函数的定义，提出了它们的基本性质，并提供了算法来构建它们。提供的例子，与共识动态的关系进行了讨论，并阐述了未来的发展方向。
Piecewise-Linear in Rates (PWLR) Lyapunov functions are introduced for a class of Complex Reaction Networks (CRNs). In addition to their simple structure, these functions are robust with respect to arbitrary monotone reaction rates, of which mass-action is a special case. The existence of such functions ensures the convergence of trajectories towards equilibria, and guarantee their asymptotic stability with respect to the corresponding stoichiometric compatibility class. We give the definition of these Lyapunov functions, present their basic properties, and provide algorithms for constructing them. Examples are provided, relationship with consensus dynamics are discussed, and future directions are elaborated.