TITLE:
Bifurcations and strange attractors in the Lorenz-84
climate model with seasonal forcing
AUTHORS:
Henk Broer (broer@math.rug.nl)
Dept. of Mathematics, University of Groningen,
PO Box 800, 9700 AV Groningen, The Netherlands,
Carles Sim\'o (carles@maia.ub.es)
Dept. de Matem\`atica Aplicada i An\`alisi, Universitat
de Barcelona, Gran Via 585, 08007 Barcelona, Spain
and
Renato Vitolo (renato@math.rug.nl)
Dept. of Mathematics, University of Groningen,
PO Box 800, 9700 AV Groningen, The Netherlands,
ABSTRACT:
A low dimensional model of general circulation of the atmosphere is
investigated. The differential equations are subject to periodic forcing,
where the period is one year. A three dimensional Poincar\'e mapping
$\mathscr{P}$ depends on three control parameters $F,$ $G,$ and $\eps$, the
latter being the relative amplitude of the oscillating part of the forcing.
This paper provides a coherent inventory of the phenomenology of
$\mathscr{P}_{F,G,\eps}$. For $\eps$ small, a Hopf-saddle-node bifurcation
$\mathcal{HSN}$ of fixed points and quasi-periodic Hopf bifurcations of
invariant circles occur, persisting from the autonomous case $\eps=0$.
For $\eps=0.5$, the above bifurcations have disappeared. Different types of
strange attractors are found in four regions (chaotic ranges) in $\{F,G\}$
and the related routes to chaos are discussed.