Properties of systems with time delayed feedback
Manffra
Elisangela Ferretti
Manffra, Elisangela Ferretti
aut
2002-04-22
2002-06-17
2014-08-12
en
<P ALIGN="justify">Nonlinear dynamics is a vast field complementary to classical
mechanics and statistical physics. Inside this field we have chosen to study dynamical
systems with time delayed feedback. Such systems appear as models in the sciences like
physics, biology, economy and have at the same time interesting theoretical properties
being good candidates to present high dimensional attractors. In this work delayed
systems are studied mainly in the limit of large delay were the scaling properties
of the attractors are observed. In chapter 2 we describe general properties of
periodic orbits of dynamical systems with feedback delay. In chapter 3 it is
shown that the marginal invariant density of chaotic attractors of scalar
systems with time delayed feedback has an asymptotic form in the limit of
large delay. We present general considerations, detailed analytical results
in low order perturbation theory for a particular model, and numerics for the
understanding of the asymptotic behaviour of the projections of the invariant
density. Our approach clarifies how the analytical properties of the model determine
the behaviour of the marginal invariant densities for large delay times. In chapter 4
properties of the topological and metric entropies are discussed and arguments for the
boundedness of both are given on the basis of periodic orbits and of the asymptotic
behavior of the invariant density. In chapter 5 we analyse the representation of maps
with time delayed feedback as coupled map lattices. We show that when the delayed map
has an anomalous exponent, this representation gives rise to infinitely large comoving
Lyapunov exponents of the spatially extended system. Additionally, we present a short
discussion regarding the anomalous error propagation in the case of continuous time,
i.e. delayed differential equations.</P>
urn:nbn:de:hbz:468-20020239
2014-08-12T08:33:56.359Z
2014-08-12T09:40:41.450Z
published
Diss
fb08/diss2002/manffra