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author:

Chen, F. (Chen, F..) [1] | Li, Z. (Li, Z..) [2] | Chen, X. (Chen, X..) [3] | Laitochová, J. (Laitochová, J..) [4]

Indexed by:

Scopus

Abstract:

In this paper, we consider a modified delay differential equation model of the growth of n-species of plankton having competitive and allelopathic effects on each other. We first obtain the sufficient conditions which guarantee the permanence of the system. As a corollary, for periodic case, we obtain a set of delay-dependent condition which ensures the existence of at least one positive periodic solution of the system. After that, by means of a suitable Lyapunov functional, sufficient conditions are derived for the global attractivity of the system. For the two-dimensional case, under some suitable assumptions, we prove that one of the components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation. Examples show the feasibility of the main results. © 2006 Elsevier B.V. All rights reserved.

Keyword:

Competition; Extinction; Global attractivity; Lyapunov functional; Permanence; Toxicology

Community:

  • [ 1 ] [Chen, F.]College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China
  • [ 2 ] [Li, Z.]College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China
  • [ 3 ] [Chen, X.]College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China
  • [ 4 ] [Laitochová, J.]Department of Mathematics, Faculty of Education, Palacký University, Olomouc, Czech Republic

Reprint 's Address:

  • [Chen, F.]College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China

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Source :

Journal of Computational and Applied Mathematics

ISSN: 0377-0427

Year: 2007

Issue: 2

Volume: 206

Page: 733-754

0 . 9 4 3

JCR@2007

2 . 1 0 0

JCR@2023

JCR Journal Grade:2

Cited Count:

WoS CC Cited Count: 0

SCOPUS Cited Count: 49

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 2

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