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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. (C) 2006 Elsevier B.V. All rights reserved.
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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
ESI Discipline: MATHEMATICS;
JCR Journal Grade:2
Cited Count:
WoS CC Cited Count: 52
SCOPUS Cited Count: 51
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 1
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