Tuesday 05 Nov 2019: Dynamics Seminar: From Lorenz to Lorenz: Principles and Possibilities in the Phase Space of Animal Behavior
Greg Stephens - VU Amsterdam
Harrison 103 13:30-15:30
Natural phenomena are teeming with temporal complexity but such dynamics, however fascinating, offer substantial obstacles to quantitative understanding. Here, we describe our progress in elucidating movement behavior in the context of a low-dimensional but complete representation of the posture of the nematode worm C. elegans. We capture these dynamics first through locally-linear models within windows determined adaptively from the data and we explore the resulting model space with a likelihood-based hierarchical clustering and the eigenvalues of the linear models. In the worm's behavior we find broad evidence of dynamical critically through a population of models fluctuating around an instability boundary. We then examine nonlinear dynamics by reconstructing a maximally predictive state space from sequences of multidimensional data: a timescale separation in which short-time sequences define the reconstructed state variables while longer-time dynamics are encoded as state space trajectories. We show the resulting state variables derived from worm foraging and discuss how the geometry and topology of these trajectories offer new understanding of C elegans locomotion, including hints of chaotic control.