scholarly journals Singularities of Invariant Densities for Random Switching between Two Linear ODEs in 2D

2021 ◽  
Vol 20 (4) ◽  
pp. 1917-1958
Author(s):  
Yuri Bakhtin ◽  
Tobias Hurth ◽  
Sean D. Lawley ◽  
Jonathan C. Mattingly
Keyword(s):  
Random Switching ◽  
Invariant Densities ◽  
Linear Odes

scholarly journals Smooth invariant densities for random switching on the torus

Nonlinearity ◽  
2018 ◽  
Vol 31 (4) ◽  
pp. 1331-1350 ◽  
Author(s):  
Yuri Bakhtin ◽  
Tobias Hurth ◽  
Sean D Lawley ◽  
Jonathan C Mattingly
Keyword(s):  
Random Switching ◽  
Invariant Densities

scholarly journals Randomly switched vector fields sharing a zero on a common invariant face

2020 ◽  
Vol 21 (02) ◽  
pp. 2150007
Author(s):  
Edouard Strickler
Keyword(s):  
Dynamical Systems ◽  
Markov Process ◽  
Lyapunov Exponents ◽  
Vector Fields ◽  
Degenerate Case ◽  
Piecewise Deterministic Markov Process ◽  
Random Switching ◽  
Invariant Densities

We consider a Piecewise Deterministic Markov Process given by random switching between finitely many vector fields vanishing at [Formula: see text]. It has been shown recently that the behavior of this process is mainly determined by the signs of Lyapunov exponents. However, results have only been given when all these exponents have the same sign. In this paper, we consider the degenerate case where the process leaves invariant some face and results are stated when the Lyapunov exponents are of opposite signs. Our results enable in particular to close a gap in a discussion on random switching between two Lorenz vector fields by Bakhtin and Hurth, Invariant densities for dynamical systems with random switching, Nonlinearity 25 (2012) 2937–2952.

scholarly journals Regularity of invariant densities for 1D systems with random switching

Nonlinearity ◽  
2015 ◽  
Vol 28 (11) ◽  
pp. 3755-3787 ◽  
Author(s):  
Yuri Bakhtin ◽  
Tobias Hurth ◽  
Jonathan C Mattingly
Keyword(s):  
Random Switching ◽  
Invariant Densities

scholarly journals Invariant densities for dynamical systems with random switching

Nonlinearity ◽  
2012 ◽  
Vol 25 (10) ◽  
pp. 2937-2952 ◽  
Author(s):  
Yuri Bakhtin ◽  
Tobias Hurth
Keyword(s):  
Dynamical Systems ◽  
Random Switching ◽  
Invariant Densities

Bases for Second Order Linear ODEs

2020 ◽  
Vol 127 (9) ◽  
pp. 849-849
Author(s):  
Peter McGrath
Keyword(s):  
Second Order ◽  
Order Linear ◽  
Linear Odes

scholarly journals Invariant densities and escape rates: Rigorous and computable approximations in the -norm

2011 ◽  
Vol 74 (13) ◽  
pp. 4481-4495 ◽  
Author(s):  
Wael Bahsoun ◽  
Christopher Bose
Keyword(s):  
Invariant Densities
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