论文标题
生物相互作用网络中非振荡行为的强大Lyapunov标准
A robust Lyapunov criterion for non-oscillatory behaviors in biological interaction networks
论文作者
论文摘要
我们介绍了非振荡的概念，提出了一种建设性的方法来进行稳健验证，并研究了其在生物相互作用网络中的应用（也称为化学反应网络）。首先，基于对非线性系统Jacobian第二添加化合物的变分系统的研究，重新访问Muldowney对周期性解决方案不存在的结果。我们表明，后者的指数稳定性排除了限制周期，准周期解决方案和广泛的振荡行为。然后，我们将重点放在具有一般动力学的生物相互作用网络中产生的非线性方程，并表明上述变分系统的动力学可以嵌入线性差分包含中。然后，我们提出了用于构建分段线性Lyapunov函数以证明全局鲁棒性非振荡行为的算法。最后，我们将技术应用于研究几个受监管的酶促循环，在可用方法无法提供有关其定性全球行为的任何信息。
We introduce the notion of non-oscillation, propose a constructive method for its robust verification, and study its application to biological interaction networks (also known as, chemical reaction networks). We begin by revisiting Muldowney's result on non-existence of periodic solutions based on the study of the variational system of the second additive compound of the Jacobian of a nonlinear system. We show that exponential stability of the latter rules out limit cycles, quasi-periodic solutions, and broad classes of oscillatory behavior. We focus then on nonlinear equations arising in biological interaction networks with general kinetics, and we show that the dynamics of the aforementioned variational system can be embedded in a linear differential inclusion. We then propose algorithms for constructing piecewise linear Lyapunov functions to certify global robust non-oscillatory behavior. Finally, we apply our techniques to study several regulated enzymatic cycles where available methods are not able to provide any information about their qualitative global behavior.
