Intermittencies and symmetry in a reverse-flow chemical reactor

(1) Dipartimento di Ingegneria Chimica, Università degli Studi di
Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli, Italia

(2) Dipartimento di Ingegneria, Università del Sannio, Piazza Roma,
82100, Benevento, Italia

(3) Dipartimento di Scienza dei Materiali ed Ingegneria Chimica,
Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129
Torino, Italia

In this work we discuss how spatio-temporal symmetry influence the dynamics of discontinuously forced chemical reactors. Recent analysis, based on Lie group theory, are related to a dynamical systems that are symmetric with respect to linear transformations that involve the system state and the time. These spatio-temporal symmetries were found in reverse-flow reactors and depend on the type of forcing only. Such symmetry properties can be used to improve efficiency and accuracy of standard bifurcational analysis, in that difficulties due to the discontinuous nature of the forcing are avoided. To this aim, suitable discrete systems based on the Poincaré map for spatio-temporal symmetric systems are constructed. Such discrete systems inherit the symmetry properties of the original systems, and are diffeomorphisms. Spatio-temporal symmetry properties influence the possible bifurcational scenarios: obviously, only some kind of bifurcations are possible, whereas some usually high-codimension bifurcations become generic. Routes to chaos also show peculiar properties: special kinds of intermittency and attractor merging crises are found and analysed.

Nonlinear models for characterisation and prediction of noisy chaotic time series

Hong Kong Polytechnic University, Hung Hom, Kowloon, zipitydoda Hong Kong SAR, China

We describe a nonlinear modelling algorithm capable of accurately
capturing dynamics from short noisy time series. This method utilises
an information theoretic model selection criteria and a variant of the
artificial neural network (ANN) modelling scheme. The ANN consists of
a single hidden layer and a monotonic nonlinear output function. The
hidden layer is composed of a relatively small number of carefully
selected neurons, the number of neurons in the optimal ANN is
determined by the minimum description length (MDL) model selection
criteria. The MDL best model is the model that captures only the
essential deterministic features of the data.

We apply this modelling algorithm to several computational are
experimental systems including chaotic differential equations, the
annual sunspot count, and a chaotic laser. In each case we show that
the optimal model captures the chaotic dynamics of the underlying
system but does not fit deterministic structure to system noise.

All volume-expanding dynamical systems have positive topological entropy

MPI for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany

One major significance of the topological entropy is its strong
relation to other dynamical invariants such as Lyapunov exponents and
Hausdorff dimension which provides our primary motivation. Almost all
previous investigations of the topological entropy have been concerned
with upper bounds, exact formulas have been derived under strong
smoothness assumptions only. In this talk we will give lower bounds of
the topological entropy of *C1*-smooth dynamical systems on
Riemannian manifolds which are in some cases sharp bounds. They are
formulated in terms of the phase space dimension and of the
exponential growth rates of a certain function of the singular values
of the tangent map. These rates correspond to the deformation of
*k*-volumes and can for instance be estimated in terms of Lyapunov
exponents. Examples address Hénon maps, the Lorenz system, the
geodesic flow on a (not necessarily compact) Riemannian manifold
without conjugate points, and skew product systems.

Dynamics Days 2002 Last modified: Tue Mar 26 16:21:45 MET 2002