Examining the evolution of phase-space elements for C.elegans locomotion

The Caenorhabditis elegans (C.elegans) nematodes have long been a model organism for quantitative behavioral analysis due to their tractable nervous system and well-characterized genetics. In particular, dynamic diffraction has been a successful method of studying said microorganisms due to its low level of noise and the ability to simultaneously study multiple degrees of freedom of their neuromuscular system through their locomotion. In this study, we estimate the Lyapunov spectrum of C.elegans locomotion, which offers an insight into how volume elements evolve in the phase space of the underlying dynamical system. For that, we used the Sano-Sawada algorithm to estimate the spectra from the trajectories reconstructed using the Takens embedding procedure. In total, two positive and one negative exponents were calculated and verified to be nonspurious through investigations of their stability for different sets of parameters. Those exponents have values of 0.860±0.028 s^{-1}, 0.389±0.014 s^{-1}, and -3.451±0.074 s^{-1}, respectively. The presence of two positive exponents indicates that C.elegans locomotion is hyperchaotic, while the total sum being negative indicates that the system is dissipative. Those are key observations for the underlying system and will be significant for the potential formulation of future mathematical or computational models.