Singularities of invariant densities for random switching between two linear ODEs in 2D

Yuri Bakhtin; Tobias Hurth; Sean D. Lawley; Jonathan C. Mattingly

doi:10.1137/20M1364345

Singularities of invariant densities for random switching between two linear ODEs in 2D

Yuri Bakhtin, Tobias Hurth, Sean D. Lawley, Jonathan C. Mattingly

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	1917-1958
Number of pages	42
Journal	SIAM Journal on Applied Dynamical Systems
Volume	20
Issue number	4
DOIs	https://doi.org/10.1137/20M1364345
State	Published - 2021

Keywords

Integral equations
Invariant densities
Randomly switched ODEs
Singularities

ASJC Scopus subject areas

Analysis
Modeling and Simulation

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10.1137/20M1364345

Cite this

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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",

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AU - Hurth, Tobias

AU - Lawley, Sean D.

AU - Mattingly, Jonathan C.

PY - 2021

Y1 - 2021

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KW - Invariant densities

KW - Randomly switched ODEs

KW - Singularities

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Singularities of invariant densities for random switching between two linear ODEs in 2D

Abstract

Keywords

ASJC Scopus subject areas

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