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On Nonlinear Dynamics of Predator-Prey Modelswith Discrete Delay

Published online by Cambridge University Press:  26 March 2009

S. Ruan
S. Ruan*
Affiliation:
Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250, USA
*
ruan@math.miami.edu
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Abstract

In this survey, we briefly review some of our recent studies on predator-preymodels with discrete delay. We first study the distribution of zeros of a seconddegree transcendental polynomial. Then we apply the general results on thedistribution of zeros of the second degree transcendental polynomial to variouspredator-prey models with discrete delay, including Kolmogorov-typepredator-prey models, generalized Gause-type predator-prey models withharvesting, etc. Bogdanov-Takens bifurcations in delayed predator-prey modelswith nonmonotone functional response and in delayed predator-prey model withpredator harvesting are also introduced.

Keywords

predator-prey modeltime delayharvestingstabilitybifurcation

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Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 4 , Issue 2: Delay equations in biology , 2009 , pp. 140 - 188
Copyright
© EDP Sciences, 2009

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