Nonstandard singular perturbation systems and higher index differential-algebraic systems.
Models of large-scale systems typically involve interacting dynamic phenomena of widely differing time-scales. These type of models may be treated as two time-scale singular perturbations systems (SPS), where the perturbation parameter is the ratio of the time-scales of the slow and fast dynamics. Tikhonov's theorem gives sufficient conditions on them to ensure a good approximation for a standard SPS, i.e., its corresponding slow system is a differential-algebraic system (DAS) of index 1. Here, it is shown that a nonstandard SPS with parameter set to zero can be seen as a DAS of higher index. This connection allows the authors to obtain a Tikhonov theorem when the DAS is of index 2.
scientific article; zbMATH DE number 1861303
scientific article