Uniform attractors of periodic and asymptotically periodic dynamical systems
The authors investigate the uniform forward global attractors of periodic systems and the comparison of the dynamics between asymptotically periodic nonautonomous dynamical systems and their corresponding limiting periodic processes. First, they construct the uniform forward global attractor \(\mathcal A\) for dissipative periodic processes. Based on this result, they show the uniform Lyapunov stability of \(\mathcal A\), establish a Lyapunov functional characterization of this stability and prove the existence of an infinitesimal positively invariant neighborhood of \(\mathcal A\). Finally, they consider various types of uniform dynamics for asymptotically periodic systems and their corresponding limiting processes. The results are illustrated with examples of ordinary and delay differential equations.
scientific article; zbMATH DE number 2154990