Prey-predator systems with delay: Hopf bifurcation and stable oscillations

This paper examines several prey-predator models with delay. It examines both existence of bounded and decaying solutions and the Hopf bifurcation of periodic orbits. Symbolic techniques are used for the computation of the stability constants via the method of averaging, with minimal resort to numerics. The characteristics of the bifurcating solutions are compared with periodic with solutions known to exist via other geometric means.