Identification of critical points in transient electroconvection dynamics using tensor bundles

Abstract

We present and demonstrate a method to produce quantitative and qualitative descriptions of transient dynamics from empirical data, with the purpose of analyzing a novel transient discovered in liquid crystal electroconvection. By constructing a tensor bundle around an exemplar transient and creating a chart at every step aligned with the direction of propagation, we show that the Jacobian estimation problem can be reduced by a single dimension, relaxing data requirements and clarifying results. We apply this analysis to identify the onset of a boundary crisis in a predator–prey model. The resulting tensor bundle estimated from image data taken during a dynamical phase transition in a nematic liquid crystal details the behavior of the system along that trajectory, allowing topological analysis. Using this method, we quantify a saddle point in the phase space that drives the initial dynamics during a sudden increase in the driving voltage.