On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay

S. Ruan
2009 Mathematical Modelling of Natural Phenomena  
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
more » ... akens bifurcations in delayed predator-prey models with nonmonotone functional response and in delayed predator-prey model with predator harvesting are also introduced.
doi:10.1051/mmnp/2009009 fatcat:5zmtbcafordo7hhzlvbq4oouem