Multiple time scale behavior fast dynamics

The presence of a singular perturbation induces multiple-time-scale behavior in dynamical systems, which is characterized by the presence of both fast and slow transients in their time response. The slow response is approximated by the reduced model (2.14), while the difference between the response of the reduced model (2.14) and that of the full model (2.7)-(2.8) is the fast transient. 

Dynamic simulations were aimed at capturing the multiple-time-scale behavior revealed by the theoretical developments presented above. Figures 7.5 and 7.6 show the evolution of the mole fraction of n-butane and of the temperature on selected column stages for a small step change in the reboiler duty. Visual inspection of the plots indicates that the temperatures exhibit a fast transient,... 

Owing to the presence of the small parameter , the model in Equation (7.1) is stiff and can potentially exhibit a dynamic behavior with multiple time scales. Proceeding in a manner similar to the one adopted in Chapter 6, we define the fast time scale r = t/e and rewrite (7.1) as... 

The dynamic behavior of reaction systems often contains multiple time-scales after an initial transient period, some fast reactions can be considered nearly instantaneous relative to the... 

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