Permanence and periodicity of a delayed ratio-dependent predator–prey model with stage structure

A periodic ratio-dependent predator–prey model with time delays and stage structure for both prey and predator is investigated. It is assumed that immature individuals and mature individuals of each species are divided by a fixed age, and that immature predators do not have the ability to attack pre...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2005-03, Vol.303 (2), p.602-621
Main Authors: Xu, Rui, Chaplain, M.A.J., Davidson, F.A.
Format: Article
Language:English
Subjects:
Biological and medical sciences
Exact sciences and technology
Fundamental and applied biological sciences. Psychology
General aspects
Mathematical analysis
Mathematics
Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects)
Ordinary differential equations
Periodic solution
Permanence
Ratio-dependence
Sciences and techniques of general use
Stage structure
Time delay
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Summary:A periodic ratio-dependent predator–prey model with time delays and stage structure for both prey and predator is investigated. It is assumed that immature individuals and mature individuals of each species are divided by a fixed age, and that immature predators do not have the ability to attack prey. Sufficient conditions are derived for the permanence and existence of positive periodic solutions of the model. Numerical simulations are presented to illustrate the feasibility of our main results.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2004.08.062