Mathematics Research Institute, University of Exeter, Exeter EX4 4QF, UK.
Philos Trans A Math Phys Eng Sci. 2012 Mar 13;370(1962):1166-84. doi: 10.1098/rsta.2011.0306.
Tipping points associated with bifurcations (B-tipping) or induced by noise (N-tipping) are recognized mechanisms that may potentially lead to sudden climate change. We focus here on a novel class of tipping points, where a sufficiently rapid change to an input or parameter of a system may cause the system to 'tip' or move away from a branch of attractors. Such rate-dependent tipping, or R-tipping, need not be associated with either bifurcations or noise. We present an example of all three types of tipping in a simple global energy balance model of the climate system, illustrating the possibility of dangerous rates of change even in the absence of noise and of bifurcations in the underlying quasi-static system.
与分叉（B- tipping）相关或由噪声引起的临界点（N- tipping）是可能导致突发性气候变化的潜在机制。我们在这里关注一类新的临界点，即系统的输入或参数发生足够快的变化可能导致系统“偏离”吸引子的一个分支。这种与分叉或噪声无关的、依赖于速率的临界点移动，或 R- tipping。我们在一个简单的气候系统全球能量平衡模型中展示了所有三种类型的临界点移动的例子，说明了即使在没有噪声和基础准静态系统中没有分叉的情况下，也可能出现危险的变化率。
