Critical transitions: Arithmetic to algebra.

2012 ◽  
pp. 229-255
Author(s):  
Martha Carr
Keyword(s):  
Critical Transitions

scholarly journals Critical Transitions from Pastoralism to Ranching in Central Africa

2021 ◽  
pp. 000-000
Author(s):  
Nikolaus Schareika ◽  
Christopher Brown ◽  
Mark Moritz
Keyword(s):  
Central Africa ◽  
Critical Transitions

scholarly journals Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

2020 ◽  
Vol 42 (1) ◽  
pp. 65-84
Author(s):  
Jinzhong Ma ◽  
Yong Xu ◽  
Yongge Li ◽  
Ruilan Tian ◽  
Shaojuan Ma ◽  
...  
Keyword(s):  
Lévy Noise ◽  
Stable Model ◽  
Efficient Tool ◽  
Escape Probability ◽  
Critical Transitions ◽  
Current State ◽  
Undesirable State ◽  
Parameter Dependent ◽  
Levy Noise ◽  
The Given

AbstractIn 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 Lévy-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 Lévy 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.

scholarly journals Local ecosystem feedbacks and critical transitions in the climate

2011 ◽  
Vol 8 (3) ◽  
pp. 223-228 ◽  
Author(s):  
Max Rietkerk ◽  
Victor Brovkin ◽  
Peter M. van Bodegom ◽  
Martin Claussen ◽  
Stefan C. Dekker ◽  
...  
Keyword(s):  
Critical Transitions ◽  
Local Ecosystem
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