Temporal Divergence of C. elegans Locomotion

The nematode Caenorhabditis elegans (C. elegans) is a model organism, commonly studied due to ease of maintenance and comparative simplicity of its neurological structure. We investigate C. elegans’ locomotion using dynamic diffraction because the observed time series due to the intensity of the diffraction relates to the locomotory dynamics of the worm. Visualizing the locomotion dynamics using lag plots and recurrence plots confirms that the locomotion satisfies the chaos criteria of determinism, aperiodic orbits, bounded orbits, and sensitive dependence on initial conditions, which are all four chaos criteria outlined by David Feldman (D. Feldman, Chaos and Fractals: An Elementary Introduction (2012), p. 85). The sensitive dependence on initial conditions implies that nearby trajectories in phase space diverge. This divergence in phase space can be quantized by either the largest Lyapunov exponent (LLE) or divergence as measured by the length of the longest line parallel to the line of identity in a recurrence plot. Here, we calculate those two different types of divergence for C. elegans locomotion.