Equi-Attraction and The Continuous Dependence of Attractors on Time Delays

Abstract

Under appropriate regularity conditions it is shown that the continuous dependence of the global attractors \mathcal{A}_\tau of semi dynamical systems S^{(\tau)}(t) in C([-\tau,0];Z) with Z a Banach space and time delay \tau \in [T_*,T^*], where T_* > 0, is equivalent to the equi-attraction of the attractors. Examples and counter examples posed in this right framework are provided.