Synchronization by degenerate noise

Fuente: arXiv
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Autori principali: Liu, Xianming, Sun, Xu
Natura: Preprint
Pubblicazione: 2025
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author Liu, Xianming
Sun, Xu
author_facet Liu, Xianming
Sun, Xu
contents In this paper, we derive several criteria for (weak) synchronization by noise without the global swift transitivity property. Our sufficient conditions for (weak) synchronization are necessary and can be applied to scenarios involving degenerate or non-Gaussian noise. These results partially answer the open question posed by Flandoli et al. (Probab Theory Relat Fields 168:511-556, 2017). As an application, we prove that the weak attractor for stochastic Lorenz 63 systems driven by degenerate noise consists of a single random point provided the noise intensity is small, and there is no weak synchronization if the noise intensity is large. This indicates that a bifurcation occurs in relation to the intensity of the noise.
format Preprint
id arxiv_https___arxiv_org_abs_2512_18278
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Synchronization by degenerate noise
Liu, Xianming
Sun, Xu
Dynamical Systems
Probability
In this paper, we derive several criteria for (weak) synchronization by noise without the global swift transitivity property. Our sufficient conditions for (weak) synchronization are necessary and can be applied to scenarios involving degenerate or non-Gaussian noise. These results partially answer the open question posed by Flandoli et al. (Probab Theory Relat Fields 168:511-556, 2017). As an application, we prove that the weak attractor for stochastic Lorenz 63 systems driven by degenerate noise consists of a single random point provided the noise intensity is small, and there is no weak synchronization if the noise intensity is large. This indicates that a bifurcation occurs in relation to the intensity of the noise.
title Synchronization by degenerate noise
topic Dynamical Systems
Probability
url https://arxiv.org/abs/2512.18278