An approximation for prey-predator models with time delay

A prototype prey-predator (P-D) model in which the effective size of the predator population interacting with its prey follows an instantaneous time-delay τ regarding its total size is considered here. A simplified model was derived after substituting the approximation into the above time-delay model. In order to assess the reliability of the simplified model, we performed a comparative study of both models under a wide range of parameter values, focusing on the effect of τ on two issues: (i) the boundary (in parameter space) between the regions leading either to stable fixed points characteristic of the non-delay model, both the boundary and the periods and amplitudes obtained for the time-delay model can be fairly approximated by the corresponding results for the simplified model.