Dynamics of a Degenerately Damped Stochastic Lorenz-Stenflo System (Journal of Nonlinear Modeling and Analysis, 2024)
It seems that little has been known about the sensitivity of steadystates in stochastic systems. This paper proves the conditions for the existenceof an invariant measure in a degenerately damped stochastic Lorenz-Stenflomodel. Precisely, the solution is proved to be a nice diffusion via the Liebracket technique and non-trivial Lyapunov functions. The finiteness of theexpected positive recurrence time entails the existence problem. On the otherhand, a cut-off function is constructed to show the non-existence result througha proof by contradiction. For other interesting cases, the expected recurrencetime is shown to be infinite.
Keywords: Lorenz-Stenflo system; invariant measure; Lyapunov function; noise-induced stabilization.