A set of gammatone band-pass filters are often used to model the filtering performed by the human inner ear. For example, "BatSLAM: Simultaneous Localization and Mapping Using Biomimetic Sonar" Jan Steckel and Herbert Peremans, as well as "Biologically inspired methods in speech recognition and synthesis: closing the loop" by Trevor Bekolay both use them. However, like all filters, if you start the input signal with silence, the gammatone filter responds differently than if you started the input signal with some sort of noise. Similarly, mammals are very rarely submerged in absolute silence. The environment and internal organs generate what I would imagine to be some sort of low frequency noise. Maybe it's a low-pass filtered white-noise?
If you are trying to use gammatone filter in a model, what do you prepend the start of your signal with? In other words, how are gammatone filters typically "primed"?