Mobile defects born from an energy cascade shape the locomotive behavior of a headless animal*

The physics of behavior seeks simple descriptions of animal behavior. The field has advanced rapidly by using techniques in low dimensional dynamics distilled from computer vision. Yet, we still do not generally understand the rules which shape these emergent behavioral manifolds in the face of complicated neuro-construction --- even in the simplest of animals. In this work, we introduce a non-neuromuscular model system which is complex enough to teach us something new but also simple enough for us to understand. We discover manifolds underlying the governing dynamics shaped and stabilized by a physical mechanism: an active-elastic, inverse-energy cascade. We explore the formulation of the governing dynamics of a polarized active elastic sheet in terms of the normal modes of an elastic structure decorated by a polarized activity at every node. By incorporating a torque mediated coupling physics, we show that the power is pumped from the shortest length scale up to longer length scale modes via a combination of direct mode coupling and preferential dissipation of higher frequency modes. We use this result to motivate the study of organismal locomotion as an emergent simplicity governing organism-scale behavior. To master the low dimensional dynamics on this manifold, we present a zero-transients limit study of the dynamics of +1 or vortex-like defects in the ciliary field (which is experimentally supported for small organisms). We show, experimentally, numerically and analytically that these defects arise from this energy cascade to generate long-lived, stable modes of locomotive behavior. Using a geometric model, we show how the defect undergoes unbinding. We extend this framework as a tool for studying larger organisms with non-circular shape and introduce local activity modulation for defect steering. We expect this work to inform the foundations of organismal control of distributed actuation without muscles or neurons.