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 m...

Reasonable sufficient conditions are obtained for the existence of positive periodic solutions in periodic delayed Gause-type predator-prey systems. Our approach involves the application of coincidence degree theorem and estimations of uniform upper bounds on solutions. This method imposes minimum restrictions on the form and magnitude of time delays. Indeed, our results are applicable to discr...

A simple mathematical homogeneous model of competition is used to describe Neanderthal extinction in Europe. It considers two interacting species, Neanderthals and Early Modern Men, in the same ecological niche. Using paleontological data we claim that the parameter of similarity, between both species, fluctuates between 0.992 and 0.997. An extension of the model including migration (diffusion)...