TITLE:
Continuation of periodic orbits in large-scale dissipative systems

AUTHORS
J. S\'anchez^(1), M. Net^(1), B. Garc{\'\i}a-Archilla^(2), C. Sim\'o^(3)

(1) Departament de F\'{\i}sica Aplicada, Universitat Polit\`ecnica de
Catalunya, Jordi Girona, 1--3, m\`odul B4--B5, Campus Nord, 08034 Barcelona
(Spain)

(2) Departamento de Matem\'atica Aplicada II, Universidad de
Sevilla, Escuela Superior de Ingenieros, Camino de los Descubrimientos, s/n,
41092 Sevilla (Spain)

(3) Departament de Matem\`atica Aplicada i An\`alisi, Universitat de Barcelona,
Gran Via de les Corts Catalanes, 585, 08071 Barcelona (Spain)

ABSTRACT
We present a numerical algorithm for the continuation of
periodic orbits of high-dimensional dissipative dynamical systems.  It
is based on single shooting and Newton-Krylov methods. A non-trivial
fluid dynamics problem, which after a pseudo-spectral discretization
gives rise to a system of dimension $O(10^4)$, has been used as test.
The efficiency of the algorithm, which allows the unfolding of a
complex bifurcation diagram of periodic orbits, shows the suitability
of the method for large-scale nonlinear dissipative partial
differential equations.