Adaptive, locally linear models of complex dynamics
Abstract
Natural phenomena are teeming with temporal complexity, but such dynamics, however fascinating, offer substantial obstacles to quantitative understanding. We introduce a general method based on the simple idea that even complicated time series are locally linear. Our analysis transforms dynamical data into a parameterized space of linear models, and we detail a hierarchical clustering of this space into dynamical categories. The linear models reveal fine-scaled, interpretable states in the posture behavior and global brain activity of the nematode Caenorhabditis elegans. Furthermore, we find that the population of stable and unstable oscillations suggests a near-critical dynamics across both brains and behavior. We expect our approach to be widely applicable.
- Publication:
-
Proceedings of the National Academy of Science
- Pub Date:
- January 2019
- DOI:
- 10.1073/pnas.1813476116
- arXiv:
- arXiv:1807.09728
- Bibcode:
- 2019PNAS..116.1501C
- Keywords:
-
- Quantitative Biology - Quantitative Methods
- E-Print:
- 25 pages, 16 figures