一类强2-正系统的整数值Lyapunov函数
The Integer-valued Lyapunov Function for a Class of Strong 2-positive Systems
杲蒙蒙 1周盾1
作者信息
- 1. 南京理工大学 数学与统计学院,南京 210094
- 折叠
摘要
针对双向循环负反馈系统对应的线性系统,即强2-正系统构造了整数值Lyapunov函数σ(·).该函数定义在ℝn中的一个开稠集上,它表示n维向量坐标之间符号改变的次数.通过定义两类与σ(·)相关的整数值函数σm(·)、σM(·),借助这些函数具有的特性,证明了σ(·)沿着解的轨道具有衰减性;同时,如此定义的整数值Lyapunov函数若满足轨道衰减性,那么所对应线性系统几乎处处是一个强2-正系统.该函数为进一步研究负反馈系统的结构稳定性以及极限集的嵌入性质等提供了有效的研究工具,对于深入了解该系统的动力学提供了重要参考.
Abstract
This article establishes an integer-valued Lyapunov function σ(·) for bidirectional negative cyclic feedback systems. The functionσ(·),defined on an open and dense subset in ℝn,represents the number of sign changes among the coordinates of an n-dimensional vector. By defining two integer-valued functions,σm(·) and σM(·),associated with σ(·) and utilizing their properties,it is demonstrated that σ(·) decays along the trajectories of solutions. At the same time,if the integer-valued Lyapunov function so defined satisfies orbital decay,then the corresponding linear system is a strong 2-positive system almost everywhere. σ(·) provides an effective research tool for further studying the structural stability and embedding prop-erties of limit sets for negative cyclic feedback systems,offering an important reference for a deeper understanding of the dynamics of such systems.
关键词
动力系统/强2-正系统/强2-合作系统/整数值Lyapunov函数Key words
dynamical system/strong 2-cooperative system/strong 2-positive system/integer-valued Lyapunov function引用本文复制引用
基金项目
国家自然科学基金(11971232)
国家自然科学基金(12071217)
出版年
2024
NETL
NSTL
万方数据