Quantifying the parameter dependent basin of the unsafe regime of asymmetric Levy-noise-induced critical transitions

• 作者: Jinzhong MA Yong XU Yongge LI Ruilan TIAN Shaojuan MA J.KURTHS
• 来源期刊: 应用数学和力学（英文版）
• 学科: 数学
• 年，卷（期）: 2021,（1）
• 页码范围: 65-84
• 页数: 20页
• 分类号: O175.13|O211.63|O29
• 语种: 英文

摘要

In real systems, the unpredictable jump changes of the random environment can induce the critical transitions (CTs) between two non-adjacent states, which are more catastrophic. Taking an asymmetric Levy-noise-induced tri-stable model with desirable, sub-desirable, and undesirable states as a prototype class of real systems, a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out. We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability, which is named as the absorbed region. Then, a new concept of the parameter dependent basin of the unsafe regime (PDBUR) under the asymmetric Levy noise is introduced. It is an efficient tool for approximately quantifying the ranges of the parameters, where the noise-induced CTs from the desirable state directly to the undesirable one may occur. More importantly, it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.