NONAUTONOMOUS CHEMOSTATS WITH VARIABLE DELAYS

被引：27

作者：

Caraballo, Tomas ^{[1
]}

Han, Xiaoying ^{[2
]}

Kloeden, Peter E. ^{[3
,4
]}

机构：

[1] Univ Seville, Dept Ecuaciones Diferenciales & Anal Numer, E-41080 Seville, Spain

[2] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA

[3] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[4] TU Kaiserslautern, Felix Klein Zentrum Math, D-67663 Kaiserslautern, Germany

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2015年 / 47卷 / 03期

关键词：

chemostat; variable delay; Lyapunov function; nonautonomous attractor; Razumikhin method; GLOBAL ASYMPTOTIC-BEHAVIOR; DIFFERENTIAL REMOVAL RATES; DISTRIBUTED DELAY; DYNAMICAL-SYSTEMS; PULLBACK ATTRACTORS; DISCRETE DELAYS; TIME-DELAY; MODEL; COMPETITION; POPULATION;

D O I：

10.1137/14099930X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The appearance of delay terms in a chemostat model can be fully justified since the future behavior of a dynamical system does not in general depend only on the present but also on its history. Sometimes only a short piece of history provides the relevant influence (bounded or finite delay), while in other cases it is the whole history that has to be taken into account (unbounded or infinite delay). In this paper a chemostat model with time variable delays and wall growth, hence a nonautonomous problem, is investigated. The analysis provides sufficient conditions for the asymptotic stability of nontrivial equilibria of the chemostat with variable delays, as well as for the existence of nonautonomous pullback attractors.

引用

页码：2178 / 2199

页数：22

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