微分代数系统的渐近性

陈伯山;廖晓昕;刘永清

系统科学与数学 ›› 2001, Vol. 21 ›› Issue (1) : 48-057.

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系统科学与数学 ›› 2001, Vol. 21 ›› Issue (1) : 48-057. DOI: 10.12341/jssms09828
论文

微分代数系统的渐近性

    陈伯山(1),廖晓昕(1),刘永清(2)
作者信息 +

ASYMPTOTIC BEHMIORS FOR ALGEBRAIC-DIFFERENTIAL SYSTEMS

    Bo Shan CHEN(1),Xiao Xin LIAO(1),Yong Qing LIU(2)
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摘要

从动力系统的角度研究微分代数系统,利用单调流理论中的结果和方法讨论微分代数系统渐近性态.首先,把所考察的系统嵌入到一族相关的系统,引进使得系统族中的每个系统生成单调流的相应偏序和条件.然后给出了若干关于解收敛于平衡点的一般性结果,并对一类微分代数系统的渐近性作了较为精细的讨论.文中结果是Hirch等关于常微分方程的相关结果的推广和改进.

Abstract

This paper is devoted to discussing asymptotic behaviors for algebraic-differential systems by the use of the monotone flow theory.First of all,a differential-algebraic system is imbedded into the entire family of the systems,and a partial order and the conditions are introduced such that the flow is monotone for each of the family.We then obtain some general results such that solution of each system to such a family converges to equilibrium,and the asymptotic behaviors of a system are discussed in some detail.Our results have generalized and improved some results shown in ordinary differential equations by Hirch et al.

关键词

微分代数系统 / 渐近性 / 单调流

Key words

Algebraic-differential system / asymptotic behaviors / monotone flow

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陈伯山 , 廖晓昕 , 刘永清. 微分代数系统的渐近性. 系统科学与数学, 2001, 21(1): 48-057. https://doi.org/10.12341/jssms09828
Bo Shan CHEN , Xiao Xin LIAO , Yong Qing LIU. ASYMPTOTIC BEHMIORS FOR ALGEBRAIC-DIFFERENTIAL SYSTEMS. Journal of Systems Science and Mathematical Sciences, 2001, 21(1): 48-057 https://doi.org/10.12341/jssms09828
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