Dynamical analysis of a chemostat model with delayed response in growth and pulse input in polluted environment

被引：21

作者：

Jiao, Jianjun ^{[1
]}

Chen, Lansun ^{[2
]}

机构：

[1] Guizhou Coll Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Sch Math & Stat, Guiyang 550004, Peoples R China

[2] Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China

来源：

JOURNAL OF MATHEMATICAL CHEMISTRY | 2009年 / 46卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Chemostat model; Delayed response in growth; Pulse input in polluted environment; Extinction; Permanence; QUALITATIVE APPROACH; POPULATIONS; TOXICANT; COMPETITION; NUTRIENT;

D O I：

10.1007/s10910-008-9474-4

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

In this paper, a chemostat model with delayed response in growth and pulse input in polluted environment is considered. Using the discrete dynamical system determined by the stroboscopic map, we obtain a microorganism-extinction periodic solution. Further, it is globally attractive. The permanent condition of the investigated system is also obtained by the theory on impulsive delay differential equation. Our results reveal that the delayed response in growth plays an important role on the outcome of the chemostat.

引用

页码：502 / 513

页数：12

共 29 条

[1]

[Anonymous], 1995, THEORY CHEMOSTAT DYN

[2]

Bainov D., 1993, IMPULSIVE DIFFERENTI, V66

[3]

Bulert G.L., 1985, SIAM J APPL MATH, V45, P435

[4] EFFECT OF TIME-DELAY AND GROWTH-RATE INHIBITION IN BACTERIAL TREATMENT OF WASTEWATER [J].

BUSH, AW ;

COOK, AE .

JOURNAL OF THEORETICAL BIOLOGY, 1976, 63 (02) :385-395

[5] THE HISTORY OF THE VEDALIA BEETLE IMPORTATION TO CALIFORNIA AND ITS IMPACT ON THE DEVELOPMENT OF BIOLOGICAL-CONTROL [J].

CALTAGIRONE, LE .

ANNUAL REVIEW OF ENTOMOLOGY, 1989, 34 :1-16

[6] EFFECTS OF TOXICANTS ON POPULATIONS - A QUALITATIVE APPROACH .4. RESOURCE CONSUMER TOXICANT MODELS [J].

DELUNA, JT ;

HALLAM, TG .

ECOLOGICAL MODELLING, 1987, 35 (3-4) :249-273

[7]

Dubey B, 1997, INDIAN J PURE AP MAT, V28, P1

[8] A theoretical and empirical investigation of delayed growth response in the continuous culture of bacteria [J].

Ellermeyer, S ;

Hendrix, J ;

Ghoochan, N .

JOURNAL OF THEORETICAL BIOLOGY, 2003, 222 (04) :485-494

[9] COMPETITION IN THE CHEMOSTAT - GLOBAL ASYMPTOTIC-BEHAVIOR OF A MODEL WITH DELAYED-RESPONSE IN GROWTH [J].

ELLERMEYER, SF .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1994, 54 (02) :456-465

[10] MODELS FOR THE EFFECT OF TOXICANT IN SINGLE-SPECIES AND PREDATOR-PREY SYSTEMS [J].

FREEDMAN, HI ;

SHUKLA, JB .

JOURNAL OF MATHEMATICAL BIOLOGY, 1991, 30 (01) :15-30

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