376 research outputs found
The Necessity for a Time Local Dimension in Systems with Time Varying Attractors
We show that a simple non-linear system of ordinary differential equations
may possess a time varying attractor dimension. This indicates that it is
infeasible to characterize EEG and MEG time series with a single time global
dimension. We suggest another measure for the description of non-stationary
attractors.Comment: 13 Postscript pages, 12 Postscript figures (figures 3b and 4 by
request from Y. Ashkenazy: [email protected]
Local estimates for entropy densities in coupled map lattices
We present a method to derive an upper bound for the entropy density of
coupled map lattices with local interactions from local observations. To do
this, we use an embedding technique being a combination of time delay and
spatial embedding. This embedding allows us to identify the local character of
the equations of motion. Based on this method we present an approximate
estimate of the entropy density by the correlation integral.Comment: 4 pages, 5 figures include
The quasi-periodic doubling cascade in the transition to weak turbulence
The quasi-periodic doubling cascade is shown to occur in the transition from
regular to weakly turbulent behaviour in simulations of incompressible
Navier-Stokes flow on a three-periodic domain. Special symmetries are imposed
on the flow field in order to reduce the computational effort. Thus we can
apply tools from dynamical systems theory such as continuation of periodic
orbits and computation of Lyapunov exponents. We propose a model ODE for the
quasi-period doubling cascade which, in a limit of a perturbation parameter to
zero, avoids resonance related problems. The cascade we observe in the
simulations is then compared to the perturbed case, in which resonances
complicate the bifurcation scenario. In particular, we compare the frequency
spectrum and the Lyapunov exponents. The perturbed model ODE is shown to be in
good agreement with the simulations of weak turbulence. The scaling of the
observed cascade is shown to resemble the unperturbed case, which is directly
related to the well known doubling cascade of periodic orbits
Epigenetic Landscape of Interacting Cells: A Model Simulation for Developmental Process
We propose a physical model for developmental process at cellular level to
discuss the mechanism of epigenetic landscape. In our simplified model, a
minimal model, the network of the interaction among cells generates the
landscape epigenetically and the differentiation in developmental process is
understood as a self-organization. The effect of the regulation by gene
expression which is a key ingredient in development is renormalized into the
interaction and the environment. At earlier stage of the development the energy
landscape of the model is rugged with small amplitude. The state of cells in
such a landscape is susceptible to fluctuations and not uniquely determined.
These cells are regarded as stem cells. At later stage of the development the
landscape has a funnel-like structure corresponding to the canalization in
differentiation. The rewinding or stability of the differentiation is also
demonstrated by substituting test cells into the time sequence of the model
development.Comment: The discussion, in terms of our model, on the recently reported
context-dependent behavior of STAP cells [Nature 505, 641-647 (2014)] has
been added in Appendi
Testing For Nonlinearity Using Redundancies: Quantitative and Qualitative Aspects
A method for testing nonlinearity in time series is described based on
information-theoretic functionals -- redundancies, linear and nonlinear forms
of which allow either qualitative, or, after incorporating the surrogate data
technique, quantitative evaluation of dynamical properties of scrutinized data.
An interplay of quantitative and qualitative testing on both the linear and
nonlinear levels is analyzed and robustness of this combined approach against
spurious nonlinearity detection is demonstrated. Evaluation of redundancies and
redundancy-based statistics as functions of time lag and embedding dimension
can further enhance insight into dynamics of a system under study.Comment: 32 pages + 1 table in separate postscript files, 12 figures in 12
encapsulated postscript files, all in uuencoded, compressed tar file. Also
available by anon. ftp to santafe.edu, in directory pub/Users/mp/qq. To be
published in Physica D., [email protected]
Iterated maps for clarinet-like systems
The dynamical equations of clarinet-like systems are known to be reducible to
a non-linear iterated map within reasonable approximations. This leads to time
oscillations that are represented by square signals, analogous to the Raman
regime for string instruments. In this article, we study in more detail the
properties of the corresponding non-linear iterations, with emphasis on the
geometrical constructions that can be used to classify the various solutions
(for instance with or without reed beating) as well as on the periodicity
windows that occur within the chaotic region. In particular, we find a regime
where period tripling occurs and examine the conditions for intermittency. We
also show that, while the direct observation of the iteration function does not
reveal much on the oscillation regime of the instrument, the graph of the high
order iterates directly gives visible information on the oscillation regime
(characterization of the number of period doubligs, chaotic behaviour, etc.)
Scale Invariance in the Nonstationarity of Physiological Signals
We introduce a segmentation algorithm to probe temporal organization of
heterogeneities in human heartbeat interval time series. We find that the
lengths of segments with different local values of heart rates follow a
power-law distribution. This scale-invariant structure is not a simple
consequence of the long-range correlations present in the data. We also find
that the differences in mean heart rates between consecutive segments display a
common functional form, but with different parameters for healthy individuals
and for patients with heart failure. This finding may provide information into
the way heart rate variability is reduced in cardiac disease.Comment: 13 pages, 5 figures, corrected typo
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