Robustness of $ \mathcal D $–pullback exponentially $ \kappa $–dissipative dynamical systems with perturbations

In this paper, we study the robustness of $ \mathcal D $–pullback exponentially $ \kappa $–dissipative dynamical systems with perturbed parameters $ \varepsilon\in E\, (\subset \mathbb{R}) $. To this end, some necessary abstract results are established. First, for each $ \varepsilon\in E $, we construct a family of compact sets $ \{ \mathscr A_ \varepsilon(t)\}_{t\in \mathbb{R}} $, which is positive invariant, pullback exponentially attracting and equi–continuous. Then, we give some technique methods for verifying $ \mathcal D $–pullback exponential $ \kappa $–dissipation. Finally, we apply our result to a nonautonomous nonclassical diffusion equation with perturbations.