Singularities of invariant densities for random switching between two linear ODEs in 2D
Dynamical Systems
2020-09-04 v1 Probability
Abstract
We consider a planar dynamical system generated by two stable linear vector fields with distinct fixed points and random switching between them. We characterize singularities of the invariant density in terms of the switching rates and contraction rates. We prove boundedness away from those singularities. We also discuss some motivating biological examples.
Cite
@article{arxiv.2009.01299,
title = {Singularities of invariant densities for random switching between two linear ODEs in 2D},
author = {Yuri Bakhtin and Tobias Hurth and Sean D. Lawley and Jonathan C. Mattingly},
journal= {arXiv preprint arXiv:2009.01299},
year = {2020}
}
Comments
36 pages, 1 figure