3,163 research outputs found
The dynamics of a low-order coupled ocean-atmosphere model
A system of five ordinary differential equations is studied which combines
the Lorenz-84 model for the atmosphere and a box model for the ocean. The
behaviour of this system is studied as a function of the coupling parameters.
For most parameter values, the dynamics of the atmosphere model is dominant.
For a range of parameter values, competing attractors exist. The Kaplan-Yorke
dimension and the correlation dimension of the chaotic attractor are
numerically calculated and compared to the values found in the uncoupled Lorenz
model. In the transition from periodic behaviour to chaos intermittency is
observed. The intermittent behaviour occurs near a Neimark-Sacker bifurcation
at which a periodic solution loses its stability. The length of the periodic
intervals is governed by the time scale of the ocean component. Thus, in this
regime the ocean model has a considerable influence on the dynamics of the
coupled system.Comment: 20 pages, 15 figures, uses AmsTex, Amssymb and epsfig package.
Submitted to the Journal of Nonlinear Scienc
The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit
The effect of small forced symmetry breaking on the dynamics near a structurally stable heteroclinic
cycle connecting two equilibria and a periodic orbit is investigated. This type of system is known
to exhibit complicated, possibly chaotic dynamics including irregular switching of sign of various
phase space variables, but details of the mechanisms underlying the complicated dynamics have
not previously been investigated. We identify global bifurcations that induce the onset of chaotic
dynamics and switching near a heteroclinic cycle of this type, and by construction and analysis
of approximate return maps, locate the global bifurcations in parameter space. We find there is a
threshold in the size of certain symmetry-breaking terms below which there can be no persistent
switching. Our results are illustrated by a numerical example
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