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Title: Sensitivity of steady states in a degenerately damped stochastic Lorenz system
We study stability of solutions for a randomly driven and degenerately damped version of the Lorenz ’63 model. Specifically, we prove that when damping is absent in one of the temperature components, the system possesses a unique invariant probability measure if and only if noise acts on the convection variable. On the other hand, if there is a positive growth term on the vertical temperature profile, we prove that there is no normalizable invariant state. Our approach relies on the derivation and analysis of nontrivial Lyapunov functions which ensure positive recurrence or null-recurrence/transience of the dynamics.
Authors:
; ;
Award ID(s):
1816551
Publication Date:
NSF-PAR ID:
10318763
Journal Name:
Stochastics and Dynamics
Volume:
21
Issue:
08
ISSN:
0219-4937
Sponsoring Org:
National Science Foundation
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