The role of multistability and transient trajectories in networked dynamical systems: Connectomic dynamics of C. elegans and behavioral assays

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 longtimescale 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.