Before revision:  Finally, we find that the interplay of non-normality and zero dynamics of the system is important in determining the pulse characteristics in response to an input. These results should be useful in analysis, to screen for pulsed dynamics in biomolecular circuits, and in design, by highlighting tunable system properties .
After revision:  Finally, we illustrate how these methods can be used to provide analytical support to numerical screens for pulsing dynamics as well as provide guidelines for design .