Math. Model. Nat. Phenom.
Volume 4, Number 2, 2009Delay equations in biology
|Page(s)||140 - 188|
|Published online||26 March 2009|
On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay
Department of Mathematics, University of Miami, Coral Gables, FL
Corresponding author: email@example.com
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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