195 research outputs found
Validity of numerical trajectories in the synchronization transition of complex systems
We investigate the relationship between the loss of synchronization and the
onset of shadowing breakdown {\it via} unstable dimension variability in
complex systems. In the neighborhood of the critical transition to strongly
non-hyperbolic behavior, the system undergoes on-off intermittency with respect
to the synchronization state. There are potentially severe consequences of
these facts on the validity of the computer-generated trajectories obtained
from dynamical systems whose synchronization manifolds share the same
non-hyperbolic properties.Comment: 4 pages, 4 figure
Model for tumour growth with treatment by continuous and pulsed chemotherapy
Peer reviewedPreprin
Anomalous synchronization threshold in coupled logistic maps
We consider regular lattices of coupled chaotic maps. Depending on lattice
size, there may exist a window in parameter space where complete
synchronization is eventually attained after a transient regime. Close outside
this window, an intermittent transition to synchronization occurs. While
asymptotic transversal Lyapunov exponents allow to determine the
synchronization threshold, the distribution of finite-time Lyapunov exponents,
in the vicinity of the critical frontier, is expected to provide relevant
information on phenomena such as intermittency. In this work we scrutinize the
distribution of finite-time exponents when the local dynamics is ruled by the
logistic map . We obtain a theoretical estimate for the
distribution of finite-time exponents, that is markedly non-Gaussian. The
existence of correlations, that spoil the central limit approximation, is shown
to modify the typical intermittent bursting behavior. The present scenario
could apply to a wider class of systems with different local dynamics and
coupling schemes.Comment: 6 pages, 6 figure
Bursting synchronization in networks with long-range coupling mediated by a diffusing chemical substance
Many networks of physical and biological interest are characterized by a
long-range coupling mediated by a chemical which diffuses through a medium in
which oscillators are embedded. We considered a one-dimensional model for this
effect for which the diffusion is fast enough so as to be implemented through a
coupling whose intensity decays exponentially with the lattice distance. In
particular, we analyzed the bursting synchronization of neurons described by
two timescales (spiking and bursting activity), and coupled through such a
long-range interaction network. One of the advantages of the model is that one
can pass from a local (Laplacian) type of coupling to a global (all-to-all) one
by varying a single parameter in the interaction term. We characterized
bursting synchronization using an order parameter which undergoes a transition
as the coupling parameters are changed through a critical value. We also
investigated the role of an external time-periodic signal on the bursting
synchronization properties of the network. We show potential applications in
the control of pathological rhythms in biological neural networks.Comment: 13 figure
Quasiparticle Interactions in Fractional Quantum Hall Systems: Justification of Different Hierarchy Schemes
The pseudopotentials describing the interactions of quasiparticles in
fractional quantum Hall (FQH) states are studied. Rules for the identification
of incompressible quantum fluid ground states are found, based upon the form of
the pseudopotentials. States belonging to the Jain sequence nu=n/(1+2pn), where
n and p are integers, appear to be the only incompressible states in the
thermodynamic limit, although other FQH hierarchy states occur for finite size
systems. This explains the success of the composite Fermion picture.Comment: RevTeX, 10 pages, 7 EPS figures, submitted fo Phys.Rev.
Colossal dielectric constants in transition-metal oxides
Many transition-metal oxides show very large ("colossal") magnitudes of the
dielectric constant and thus have immense potential for applications in modern
microelectronics and for the development of new capacitance-based
energy-storage devices. In the present work, we thoroughly discuss the
mechanisms that can lead to colossal values of the dielectric constant,
especially emphasising effects generated by external and internal interfaces,
including electronic phase separation. In addition, we provide a detailed
overview and discussion of the dielectric properties of CaCu3Ti4O12 and related
systems, which is today's most investigated material with colossal dielectric
constant. Also a variety of further transition-metal oxides with large
dielectric constants are treated in detail, among them the system La2-xSrxNiO4
where electronic phase separation may play a role in the generation of a
colossal dielectric constant.Comment: 31 pages, 18 figures, submitted to Eur. Phys. J. for publication in
the Special Topics volume "Cooperative Phenomena in Solids: Metal-Insulator
Transitions and Ordering of Microscopic Degrees of Freedom
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