Contribution to the study of the effect of the interspecificity on a two nutrients competition model

被引：5

作者：

Borsali, Fethi ^{[1
]}

Yadi, Karim ^{[1
]}

机构：

[1] Univ Tlemcen, Dynam Syst & Applicat Lab, Tilimsen 13000, Algeria

来源：

INTERNATIONAL JOURNAL OF BIOMATHEMATICS | 2015年 / 8卷 / 01期

关键词：

Dynamical systems; chemostat; local stability; uniform persistence; complementary nutrients; interspecific interaction; EXPLOITATIVE COMPETITION; COMPLEMENTARY; CHEMOSTAT; STABILITY;

D O I：

10.1142/S1793524515500084

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We consider a model of the exploitative competition of two micro-organisms for two complementary nutrients in a chemostat and take into account the interspecific interaction. The growth functions occurring in the model are of general type and the interaction functions are monotonic and positive. By the mean of the Thieme-Zhao theorem, we establish conditions for uniform persistence of the model.

引用

页数：17

共 14 条

[1] EXPLOITATIVE COMPETITION IN A CHEMOSTAT FOR 2 COMPLEMENTARY, AND POSSIBLY INHIBITORY, RESOURCES [J].

BUTLER, GJ ;

WOLKOWICZ, GSK .

MATHEMATICAL BIOSCIENCES, 1987, 83 (01) :1-48

[2] ECOLOGICAL ECONOMICS OF FORAGING AMONG COEVOLVING ANIMALS AND PLANTS [J].

COVICH, A .

ANNALS OF THE MISSOURI BOTANICAL GARDEN, 1974, 61 (03) :794-805

[3] VONLIEBIG LAW OF THE MINIMUM AND PLANKTON ECOLOGY (1899-1991) [J].

DEBAAR, HJW .

PROGRESS IN OCEANOGRAPHY, 1994, 33 (04) :347-386

[4]

Gail S K Wolkowicz, 1998, 生物数学学报, V13, P282

[5] EXPLOITATIVE COMPETITION OF MICROORGANISMS FOR 2 COMPLEMENTARY NUTRIENTS IN CONTINUOUS CULTURES [J].

HSU, SB ;

CHENG, KS ;

HUBBELL, SP .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1981, 41 (03) :422-444

[6] COMPETITION BETWEEN 2 SPECIES FOR 2 COMPLEMENTARY OR SUBSTITUTABLE RESOURCES [J].

LEON, JA ;

TUMPSON, DB .

JOURNAL OF THEORETICAL BIOLOGY, 1975, 50 (01) :185-201

[7] Global asymptotic behavior of the chemostat: General response functions and different removal rates [J].

Li, BT .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1998, 59 (02) :411-422

[8] Stability and stabilization for models of chemostats with multiple limiting substrates [J].

Mazenc, Frederic ;

Malisoff, Michael .

JOURNAL OF BIOLOGICAL DYNAMICS, 2012, 6 (02) :612-627

[9] OPTIMIZATION MODEL OF FOOD SELECTION [J].

RAPPORT, DJ .

AMERICAN NATURALIST, 1971, 105 (946) :575-&

[10]

Smith H.L., 1995, The theory of the chemostat: dynamics of microbial competition, V13

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