  First return maps of interspike intervals for biological neurons that
generate repetitive bursts of impulses can display stereotyped structures
(neuronal signatures). Such structures have been linked to the possibility of
multicoding and multifunctionality in neural networks that produce and control
rhythmical motor patterns. In some cases, isolating the neurons from their
synaptic network revealsirregular, complex signatures that have been regarded
as evidence of intrinsic, chaotic behavior.
  We show that incorporation of dynamical noise into minimal neuron models of
square-wave bursting (either conductance-based or abstract) produces signatures
akin to those observed in biological examples, without the need for fine-tuning
of parameters or ad hoc constructions for inducing chaotic activity. The form
of the stochastic term is not strongly constrained, and can approximate several
possible sources of noise, e.g. random channel gating or synaptic bombardment.
  The cornerstone of this signature generation mechanism is the rich,
transient, but deterministic dynamics inherent in the square-wave
(saddle-node/homoclinic) mode of neuronal bursting. We show that noise causes
the dynamics to populate a complex transient scaffolding or skeleton in state
space, even for models that (without added noise) generate only periodic
activity (whether in bursting or tonic spiking mode).
