A deterministic continuous-time predator-prey model is analyzed considering the use of refuge by a part of prey population. In earlier works it has been claimed that the prey refuge use exerts a stabilizing effect in the dynamics of the interacting populations. In this work, we show that the above statement it is true assuming that the quantity of prey in refuge considering that this quantity is described by a function proportional to encounters between prey and predators r X XY   and we analyze the dynamic properties of such a system through modifying the well-known Lotka-Volterra predator-prey model.

In this paper we make an analysis of a generalization of van der Pol equation without periodic orbits in a domain on the plane. We use a Gasull's result and Dulac's criterion. Mathematics Subject Classification: 34A34