On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay∗

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.