Resonators prefer certain (resonant) frequency of the incoming pulses (band-pass filtering). Increasing the frequency may delay or even terminate their response.
Integrators do not have this property.
Resonators have been discovered, e.g., in
Thalamus: Hutcheon et al. 1994, Puil et al. 1994
Cortex: Llinas, Grace, Yarom 1991,
Gutfreund et al. 1995, Hutcheon et al. 1996
Review: Hutcheon and Yarom