Chaotic and non-chaotic response to quasiperiodic forcing: limits to predictability of ice ages paced by Milankovitch forcing
Ashwin, PB; Camp, CD; von der Heydt, AS
Date: 8 May 2018
Journal
Dynamics and Statistics of the Climate System
Publisher
Oxford University Press (OUP)
Publisher DOI
Abstract
It is well known that periodic forcing of a nonlinear system, even of a two-dimensional
autonomous system, can produce chaotic responses with sensitive dependence on initial
conditions if the forcing induces sufficient stretching and folding of the phase space.
Quasiperiodic forcing can similarly produce chaotic responses, where the ...
It is well known that periodic forcing of a nonlinear system, even of a two-dimensional
autonomous system, can produce chaotic responses with sensitive dependence on initial
conditions if the forcing induces sufficient stretching and folding of the phase space.
Quasiperiodic forcing can similarly produce chaotic responses, where the transition to
chaos on changing a parameter can bring the system into regions of strange non-chaotic
behaviour. Although it is generally acknowledged that the timings of Pleistocene ice
ages are at least partly due to Milankovitch forcing (which may be approximated as
quasiperiodic, with energy concentrated near a small number of frequencies), the precise
details of what can be inferred about the timings of glaciations and deglaciations
from the forcing is still unclear. In this paper, we perform a quantitative comparison
of the response of several low-order nonlinear conceptual models for these ice ages
to various types of quasiperiodic forcing. By computing largest Lyapunov exponents
and mean periods, we demonstrate that many models can have a chaotic response to
quasiperiodic forcing for a range of forcing amplitudes, even though some of the simplest
conceptual models do not. These results suggest that pacing of ice ages to forcing
may have only limited determinism.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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