150 research outputs found
Intrinsic unpredictability of strong El Ni\~no events
The El Ni\~no-Southern Oscillation (ENSO) is a mode of interannual
variability in the coupled equatorial ocean/atmosphere Pacific. El Ni\~no
describes a state in which sea surface temperatures in the eastern Pacific
increase and upwelling of colder, deep waters diminishes. El Ni\~no events
typically peak in boreal winter, but their strength varies irregularly on
decadal time scales. There were exceptionally strong El Ni\~no events in
1982-83, 1997-98 and 2015-16 that affected weather on a global scale. Widely
publicized forecasts in 2014 predicted that the 2015-16 event would occur a
year earlier. Predicting the strength of El Ni\~no is a matter of practical
concern due to its effects on hydroclimate and agriculture around the world.
This paper presents a new robust mechanism limiting the predictability of
strong ENSO events: the existence of an irregular switching between an
oscillatory state that has strong El Ni\~no events and a chaotic state that
lacks strong events, which can be induced by very weak seasonal forcing or
noise.Comment: 4 pages, 6 figure
Homoclinic Orbits of the FitzHugh-Nagumo Equation: The Singular-Limit
The FitzHugh-Nagumo equation has been investigated with a wide array of
different methods in the last three decades. Recently a version of the
equations with an applied current was analyzed by Champneys, Kirk, Knobloch,
Oldeman and Sneyd using numerical continuation methods. They obtained a
complicated bifurcation diagram in parameter space featuring a C-shaped curve
of homoclinic bifurcations and a U-shaped curve of Hopf bifurcations. We use
techniques from multiple time-scale dynamics to understand the structures of
this bifurcation diagram based on geometric singular perturbation analysis of
the FitzHugh-Nagumo equation. Numerical and analytical techniques show that if
the ratio of the time-scales in the FitzHugh-Nagumo equation tends to zero,
then our singular limit analysis correctly represents the observed
CU-structure. Geometric insight from the analysis can even be used to compute
bifurcation curves which are inaccessible via continuation methods. The results
of our analysis are summarized in a singular bifurcation diagram.Comment: preprint version - for final version see journal referenc
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