Time delay in prey-predator models

Abstract In deterministic models of prey-predator interaction, it is natural to include a time delay in the term giving the dependence of dN 2 dt on N1, where are the populations of prey and predator. This yields an integro-differential equation. Two ways are given of reducing this to one or more ordinary differential equations. Lotka-Volterra cycles are unstable, but the Lotka-Volterra model with limited prey population can yield a limit cycle when time delay is included. A model due to May continues to give limit cycles at least for moderate time delays. In this model, for certain ranges of the parameters, a limit cycle may appear for moderate time delays, although absent both in the instantaneous limit and for long time delays.