@article{530d78c73d234169bd346a2d87108915,
title = "Singularities of invariant densities for random switching between two linear ODEs in 2D",
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.",
keywords = "Integral equations, Invariant densities, Randomly switched ODEs, Singularities",
author = "Yuri Bakhtin and Tobias Hurth and Lawley, {Sean D.} and Mattingly, {Jonathan C.}",
note = "Funding Information: \ast Received by the editors September 4, 2020; accepted for publication (in revised form) July 8, 2021; published electronically October 11, 2021. https://doi.org/10.1137/20M1364345 Funding: The work of the first author was partially supported by NSF grants DMS-1460595 and DMS-1811444. The work of the second author was supported by SNF grant 200021-175728/1. The work of the third author was partially supported by NSF grants DMS-1944574 and DMS-1814832. The work of the fourth author was partially supported by NSF grant DMS-1613337. \dagger Courant Institute of Mathematical Sciences, New York University, New York, NY 10012-1185 USA (bakhtin@ cims.nyu.edu). \ddagger Institut de math\e'matiques, Universit\e' de Neuch\{\^a}tel, CH-2000 Neuch\{\^a}tel, Switzerland (tobiashurth@gmail.com). \S Department of Mathematics, University of Utah, Salt Lake City, UT 84112 USA (lawley@math.utah.edu). \P Mathematics Department and Department of Statistical Science, Duke University, Durham, NC 27708 USA (jonathan.mattingly@duke.edu). Publisher Copyright: {\textcopyright} 2021 Society for Industrial and Applied Mathematics",
year = "2021",
doi = "10.1137/20M1364345",
language = "English (US)",
volume = "20",
pages = "1917--1958",
journal = "SIAM Journal on Applied Dynamical Systems",
issn = "1536-0040",
publisher = "Society of Industrial and Applied Mathematics",
number = "4",
}