  The neural dynamics of the nematode C. elegans are experimentally
low-dimensional and correspond to discrete behavioral states, where previous
modeling work has found neural proxies for some of these states. Experimental
results further suggest that dynamics may be understood as long-timescale
transitions between multiple low-dimensional attractors. To identify
multistable regimes of our model, we develop a method for systematic generation
of bifurcation diagrams and their analysis in an interpretable low-dimensional
subspace, showing the existence and nature of multistable input responses at a
glance. Stimulation of the PLM neuron pair, experimentally associated with
forward movement and shown in simulation to drive a limit cycle, defines our
low-dimensional projection space. We then obtain bifurcation diagrams for
single-neuron excitation over a range of amplitudes and which classify whether
the dynamics in this projection space are associated with a limit cycle, fixed
point, or multiple states. In the specific case of compound input into both the
PLM pair and ASK pair we discover bistability of a limit cycle and a fixed
point, with transitional timescales between different states being much longer
than other timescales in the system. This suggests consistency of our model
with the characterization of dynamics in neural systems as long-timescale
transitions between discrete, low-dimensional attractors corresponding to
behavioral states. Our methodology thus prescribes a method for identifying
these states and transitions in response to arbitrary input.
