Stable oscillations in a predator-prey model with time lag

The Lotka-Volterra model with carrying capacity at the prey and time delay in the equation concerning the predator is considered. The time delay is taken into consideration by an integral with the weight function a exp(?at). It is shown that under certain conditions imposed upon the parameters of the system a supercritical Hopf bifurcation takes place at a certain value a₀, of a and the bifurcating closed paths are orbitally asymptotically stable for values of a below a₀.