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Retarder system is a very important class of singularly perturbed problems in the physical, biological and engineering and other fields have a wide range of important applications , such as the beating heart model , the model of nerve impulses , leaves folded model, and the storage and cytosolic calcium release , the circuit model , etc. its characteristics are dependent on two different time scales , one of the variables change much faster than the other variables , which makes it very sensitive to initial conditions . this paper describes some of the basic retarder system concepts and theories , and use singular perturbation theory techniques and methods retarder system solutions and related properties the first chapter provides a summary description of singular perturbation theory and retarder systems research background, relevant skills and methods Chapter II describes the basic theory and retarder systems of singular perturbation theory in the study of some of the retarder system applications, including retarder curve near regular solution , generalized Bonckaert standard linearization theorem, retarder system and Van der approximation solution Pol equation periodic solutions and so on.
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