Global stability for three-species Lotka–Volterra systems with delay

In this paper, a three-species delayed Lotka–Volterra system without delayed interspecific competitions is considered. It is proved that the system is globally stable for all off-diagonal delays τ ij ⩾0 ( i≠j, i,j=1,2,3 ) if and only if the interaction matrix of the system satisfies condition (WDD)....

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Bibliographic Details
Published in:Applied mathematics and computation 2003-03, Vol.135 (2), p.301-306
Main Authors: EL-Owaidy, H.M., Ismail, M.
Format: Article
Language:English
Subjects:
Biological and medical sciences
Equilibrium
Exact sciences and technology
Fundamental and applied biological sciences. Psychology
General aspects
Global analysis, analysis on manifolds
Global stability
Mathematical analysis
Mathematics
Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects)
Ordinary differential equations
Sciences and techniques of general use
Three-species
Time delay
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:In this paper, a three-species delayed Lotka–Volterra system without delayed interspecific competitions is considered. It is proved that the system is globally stable for all off-diagonal delays τ ij ⩾0 ( i≠j, i,j=1,2,3 ) if and only if the interaction matrix of the system satisfies condition (WDD).
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(01)00332-0