Susannah G. Zhang, University of Georgia, Athens, GA
Anshul Singhvi, Bard College at Simon s Rock, Great Barrington, MA
Kathleen M. Susman, Vassar College, Poughkeepsie, NY
Harold M. Hastings, Bard College at Simon s Rock, Great Barrington, MA
Jenny Magnes, Vassar College, Poughkeepsie, NY

Abstract: We describe the locomotion of Caenorhabditis elegans (C. elegans) using nonlinear dynamics. C. elegans is a commonly studied model organism based on ease of maintenance and simple neurological structure. In contrast to traditional microscopic techniques, which require constraining motion to a 2D microscope slide, dynamic diffraction allows the observation of locomotion in 3D as a time series of the intensity at a single point in the diffraction pattern. The electric field at any point in the far-field diffraction pattern is the result of a superposition of the electric fields bending around the worm. As a result, key features of the motion can be recovered by analyzing the intensity time series. One can now apply modern nonlinear techniques; embedding and recurrence plots, providing valuable insight for visualizing and comparing data sets. We found significant markers of low-dimensional chaos. Next, we implemented a minimal biomimetic simulation of the central pattern generator of C. elegans with FitzHugh-Nagumo neurons, which exhibits undulatory oscillations similar to those of the real C. elegans. Finally, we briefly describe the construction of a biomimetic version of the Izquierdo and Beer robotic worm using Keener's implementation of the Nagumo et al. circuit.

Keywords: chaos, far-field diffraction, attractor, entropy, false nearest neighbor, Lyapunov exponent, FitzHugh-Nagumo, computational modeling