  We develop a biophysical model of neuro-sensory integration in the model
organism Caenorhabditis elegans. Building on recent experimental findings of
the neuron conductances and their resolved connectome, we posit the first full
dynamic model of the neural voltage excitations that allows for a
characterization of input stimuli to behavioral responses. Thus a clear
connection between receptory cell inputs to downstream motor-responses is
illustrated, showing that robust, low-dimensional bifurcation structures
dominate neural pathways of activity. The underlying bifurcation structures
discovered, i.e. an induced Hopf bifurcation, are critical in explaining
behavioral responses such as swimming and crawling. More broadly, we
demonstrate that complex dynamical networks can produce robust functionality
from underlying low-dimensional bifurcations.
