A NEW PROOF OF THE COMPETITIVE EXCLUSION PRINCIPLE IN THE CHEMOSTAT

被引：9

作者：

Rapaport, Alain ^{[1
]}

Veruete, Mario ^{[2
]}

机构：

[1] Univ Montpellier, INRA, MISTEA, Montpellier SupAgro, 2 Pl Pierre Viala, F-34060 Montpellier, France

[2] Univ Montpellier, CNRS, IMAG, Pl Eugene Bataillon, F-34090 Montpellier, France

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2019年 / 24卷 / 08期

关键词：

Chemostat model; competitive exclusion; global stability; comparison principle; induction; GENERAL RESPONSE FUNCTIONS; MATHEMATICAL-MODEL; GLOBAL DYNAMICS; BEHAVIOR;

D O I：

10.3934/dcdsb.2018314

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give an new proof of the well-known competitive exclusion principle in the chemostat model with N species competing for a single resource, for any set of increasing growth functions. The proof is constructed by induction on the number of the species, after being ordered. It uses elementary analysis and comparisons of solutions of ordinary differential equations.

引用

页码：3755 / 3764

页数：10

共 50 条

[31] Competitive Exclusion in a General Multi-species Chemostat Model with Stochastic Perturbations
Xu, Chaoqun
Yuan, Sanling
Zhang, Tonghua
BULLETIN OF MATHEMATICAL BIOLOGY, 2021, 83 (01)
[32] COMMUNITY EQUILIBRIA AND STABILITY, AND AN EXTENSION OF COMPETITIVE EXCLUSION PRINCIPLE
LEVIN, SA
AMERICAN NATURALIST, 1970, 104 (939): : 413 - +
[33] SOME MATHEMATICAL ASPECTS OF ECOLOGICAL PRINCIPLE OF COMPETITIVE EXCLUSION
ARMSTRONGJONES, R
MCGEHEE, R
ZICARELLI, J
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (01): : A263 - A263
[34] An exclusion principle for periodic competitive systems in three dimensions
Ortega, R
Tineo, A
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1998, 31 (07) : 883 - 893
[35] Some discrete competition models and the competitive exclusion principle
Cushing, JM
Levarge, S
Chitnis, N
Henson, SM
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2004, 10 (13-15) : 1139 - 1151
[36] Exclusion principle for periodic competitive systems in three dimensions
Ortega, Rafael
Tineo, Antonio
Nonlinear Analysis, Theory, Methods and Applications, 1998, 31 (07): : 883 - 893
[37] COMPETITIVE EXCLUSION - EXCLUSION PRINCIPLE IS RECAST IN CONTEXT OF A GENERALIZED SCHEME FOR INTERSPECIFIC INTERACTIONS
PATTEN, BC
SCIENCE, 1961, 134 (349) : 1599 - &
[38] GARSIA AND MILNE BIJECTIVE PROOF OF THE INCLUSION EXCLUSION-PRINCIPLE
ZEILBERGER, D
DISCRETE MATHEMATICS, 1984, 51 (01) : 109 - 110
[39] A New Proof of the Likelihood Principle
Gandenberger, Greg
BRITISH JOURNAL FOR THE PHILOSOPHY OF SCIENCE, 2015, 66 (03): : 475 - 503
[40] A new proof of the maximum principle
Ngo Van Long
Koji Shimomura
Economic Theory, 2003, 22 (3) : 671 - 674

← 1 2 3 4 5 →