TY - JOUR
T1 - Dynamics of a Degenerately Damped Stochastic Lorenz-Stenflo System
AU - Zhou , Liangke
AU - Zeng , Caibin
JO - Journal of Nonlinear Modeling and Analysis
VL - 3
SP - 471
EP - 493
PY - 2023
DA - 2023/08
SN - 5
DO - http://doi.org/10.12150/jnma.2023.471
UR - https://global-sci.org/intro/article_detail/jnma/21947.html
KW - Lorenz-Stenflo system, invariant measure, Lyapunov function,
noise-induced stabilization.
AB - <p style="text-align: justify;">It seems that little has been known about the sensitivity of steady
states in stochastic systems. This paper proves the conditions for the existence
of an invariant measure in a degenerately damped stochastic Lorenz-Stenflo
model. Precisely, the solution is proved to be a nice diffusion via the Lie
bracket technique and non-trivial Lyapunov functions. The finiteness of the
expected positive recurrence time entails the existence problem. On the other
hand, a cut-off function is constructed to show the non-existence result through
a proof by contradiction. For other interesting cases, the expected recurrence
time is shown to be infinite.</p>