Robust exponential attractors for population dynamics models with infinite time delay

We consider an integrodifferential react ion-diffusion system which finds application in population dynamics. The memory kernels accounting for delay effects can be of both weak and strong type. Rescaling the kernels with a time relaxation epsilon > 0, we show that the original model gives raise to a one-parameter family of dynamical systems in a suitable phase-space. We prove that this family is characterized by a corresponding family of exponential attractors which is stable as the delay effects vanish, i.e., when epsilon goes to 0.