Issue |
Math. Model. Nat. Phenom.
Volume 4, Number 2, 2009
Delay equations in biology
|
|
---|---|---|
Page(s) | 140 - 188 | |
DOI | https://doi.org/10.1051/mmnp/20094207 | |
Published online | 26 March 2009 |
On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay
Department of Mathematics, University of Miami, Coral Gables, FL
33124-4250, USA
Corresponding author: ruan@math.miami.edu
In this survey, we briefly review some of our recent studies on predator-prey models with discrete delay. We first study the distribution of zeros of a second degree transcendental polynomial. Then we apply the general results on the distribution of zeros of the second degree transcendental polynomial to various predator-prey models with discrete delay, including Kolmogorov-type predator-prey models, generalized Gause-type predator-prey models with harvesting, etc. Bogdanov-Takens bifurcations in delayed predator-prey models with nonmonotone functional response and in delayed predator-prey model with predator harvesting are also introduced.
Mathematics Subject Classification: 34K18 / 92D25
Key words: predator-prey model / time delay / harvesting / stability / bifurcation
© EDP Sciences, 2009
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