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Dimensionality and Dynamics in the Behavior of C. elegans

Figure 5

Reconstructing the phase dynamics.

(A) The mean acceleration of the phase F(ω,φ) in Equation 4. (B) The correlation function of the noise 〈η (t)η(t+τ)〉. The noise correlations are confined to short times relative to the phase velocity itself. (C) Trajectories in the deterministic dynamics. A selection of early-time trajectories is shown in black. At late times these same trajectories collapse to one of four attractors (red): forward and backward crawling and two pause states. (D) Joint density ρ(ω,φ) for worms sampled at 32 Hz. A sample trajectory of a single worm moving forwards, backwards, and pausing, is denoted by black arrows.

Figure 5