Dynamics of the diffusive Nicholson's blowflies equation with distributed delay

In this paper we study the diffusive Nicholson's blowflies equation. Genera lizing previous works, we model the generation delay by using an integral c onvolution over all past times and results are obtained for general delay k ernels as far as possible. The linearized stability of the non-zero uniform steady state is studied in detail, mainly by using the principle of the ar gument. Global stability both of this state and of the zero state are studi ed by using energy methods and by employing a comparison principle for dela y equations. Finally, we consider what bifurcations are possible from the n on-zero uniform state in the case when it is unstable.