Nonstandard singularly perturbed models refer to a class of mathematical models that involve differential equations with a small parameter multiplying the highest derivative term. These models are characterized by having two distinct time scales: a fast time scale associated with the higher-order derivatives and a slow time scale associated with the lower-order derivatives.
Unlike standard singularly perturbed models, where the small parameter multiplies all the derivative terms, nonstandard singularly perturbed models have the small parameter multiplying only specific derivative terms. This leads to unique behavior and challenges in their analysis and numerical solution.
Nonstandard singularly perturbed models arise in various fields of science and engineering, including chemical kinetics, electronics, fluid dynamics, control theory, and more. Their study requires specialized techniques such as matched asymptotic expansions, boundary layer analysis, or multiple scales analysis to accurately capture the dynamics on both time scales.
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