Between Behaviors: Comparison of Two Dynamical Models of Behavioral Switching for \textit{C. Elegans} Locomotion

Organisms must manage a trade-off between robustness and flexibility as they enact adaptive behaviors. One way organisms achieve this is by navigating a network of quasi-stable behavioral states. Evidence for such behavioral states has been observed in many organisms, and new methods for detecting these states have taken on a prominent research focus. Although dynamical models demonstrating behavioral switching have been developed significantly over the past few decades, theories of the similarities and differences among these models, necessary for advancing empirical modeling, have not yet been fully elaborated. Here, we consider behavioral switching in two different classes of dynamical models of the forward-reversal behavioral transition in C. elegans. We first show how fundamentally different models can give rise to similar phenomena under noisy conditions. We then analyze the deterministic aspects of these models to expand on their differences, clarifying the theoretical relationship between them. Finally, we demonstrate how sequence models can be further extended to incorporate dwell times for behavioral states. Our work contributes toward a broader theoretical understanding of behavioral switching in adaptive systems.