Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system

@article{Ashwin2012TippingPI,
  title={Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system},
  author={P. Ashwin and S. Wieczorek and R. Vitolo and P. Cox},
  journal={Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  year={2012},
  volume={370},
  pages={1166 - 1184}
}
  • P. Ashwin, S. Wieczorek, +1 author P. Cox
  • Published 2012
  • Computer Science, Mathematics, Physics, Medicine
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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… Expand
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If M is scalar, then we can choose c = 1, β = −M, and (1.2) reduces to [1, equation (2.9)]. On the other hand, if M is a matrix, then we need a good choice of c and β in (1.1) to make the tippingExpand
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