Singularly perturbed systems with three or more time scales

On introducing the stretched fast time scale r = tje and considering the limit —0 in Equation (2.11), we also obtain the following description of the fast dynamics  

4 Singularly perturbed systems with three or more time scales 

The developments presented above have been limited to the case of a single small, singular perturbation parameter being present in the system description. However, in practical applications, e.g., the analysis of complex reaction networks (Vora 2000, Gerdtzen et al. 2004) or of processes with physical and chemical phenomena occurring at different rates (Vora and Daoutidis 2001), it is possible that several such parameters j, i 1. fc, are present. Typically, the values of these parameters are themselves of very different magnitudes, with 

In such cases, the system is said to be in a multiply singularly perturbed form, and has the potential to exhibit a dynamic behavior featuring more than two time scales. 

As in the case of two-time-scale systems, research work on systems exhibiting more than two time scales has mostly focused on the standard singularly perturbed form (Hoppensteadt 1971). Comparatively, however, such systems (and, in particular, nonstandard multiply singularly perturbed ones) have received far less attention than their two-time-scale counterparts (Vora et al. 2006). 

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