134 research outputs found
Mixed-mode oscillations in a multiple time scale phantom bursting system
In this work we study mixed mode oscillations in a model of secretion of GnRH
(Gonadotropin Releasing Hormone). The model is a phantom burster consisting of
two feedforward coupled FitzHugh-Nagumo systems, with three time scales. The
forcing system (Regulator) evolves on the slowest scale and acts by moving the
slow nullcline of the forced system (Secretor). There are three modes of
dynamics: pulsatility (transient relaxation oscillation), surge (quasi steady
state) and small oscillations related to the passage of the slow nullcline
through a fold point of the fast nullcline. We derive a variety of reductions,
taking advantage of the mentioned features of the system. We obtain two
results; one on the local dynamics near the fold in the parameter regime
corresponding to the presence of small oscillations and the other on the global
dynamics, more specifically on the existence of an attracting limit cycle. Our
local result is a rigorous characterization of small canards and sectors of
rotation in the case of folded node with an additional time scale, a feature
allowing for a clear geometric argument. The global result gives the existence
of an attracting unique limit cycle, which, in some parameter regimes, remains
attracting and unique even during passages through a canard explosion.Comment: 38 pages, 16 figure
Chaos at the border of criticality
The present paper points out to a novel scenario for formation of chaotic
attractors in a class of models of excitable cell membranes near an
Andronov-Hopf bifurcation (AHB). The mechanism underlying chaotic dynamics
admits a simple and visual description in terms of the families of
one-dimensional first-return maps, which are constructed using the combination
of asymptotic and numerical techniques. The bifurcation structure of the
continuous system (specifically, the proximity to a degenerate AHB) endows the
Poincare map with distinct qualitative features such as unimodality and the
presence of the boundary layer, where the map is strongly expanding. This
structure of the map in turn explains the bifurcation scenarios in the
continuous system including chaotic mixed-mode oscillations near the border
between the regions of sub- and supercritical AHB. The proposed mechanism
yields the statistical properties of the mixed-mode oscillations in this
regime. The statistics predicted by the analysis of the Poincare map and those
observed in the numerical experiments of the continuous system show a very good
agreement.Comment: Chaos: An Interdisciplinary Journal of Nonlinear Science
(tentatively, Sept 2008
On the approximation of the canard explosion point in singularly perturbed systems without an explicit small parameter
A canard explosion is the dramatic change of period and amplitude of a limit cycle of a system of nonlinear ODEs in a very narrow interval of the bifurcation parameter. It occurs in slow–fast systems and is well understood in singular perturbation problems where a small parameter epsilon defines the time-scale separation. We present an iterative algorithm for the determination of the canard explosion point which can be applied for a general slow–fast system without an explicit small parameter. We also present assumptions under which the algorithm gives accurate estimates of the canard explosion point. Finally, we apply the algorithm to the van der Pol equations, a Templator model for a self-replicating system and a model for intracellular calcium oscillations with no explicit small parameters and obtain very good agreement with results from numerical simulations.<br/
On the use of blow up to study regularizations of singularities of piecewise smooth dynamical systems in
In this paper we use the blow up method of Dumortier and Roussarie
\cite{dumortier_1991,dumortier_1993,dumortier_1996}, in the formulation due to
Krupa and Szmolyan \cite{krupa_extending_2001}, to study the regularization of
singularities of piecewise smooth dynamical systems
\cite{filippov1988differential} in . Using the regularization
method of Sotomayor and Teixeira \cite{Sotomayor96}, first we demonstrate the
power of our approach by considering the case of a fold line. We quickly
recover a main result of Bonet and Seara \cite{reves_regularization_2014} in a
simple manner. Then, for the two-fold singularity, we show that the regularized
system only fully retains the features of the singular canards in the piecewise
smooth system in the cases when the sliding region does not include a full
sector of singular canards. In particular, we show that every locally unique
primary singular canard persists the regularizing perturbation. For the case of
a sector of primary singular canards, we show that the regularized system
contains a canard, provided a certain non-resonance condition holds. Finally,
we provide numerical evidence for the existence of secondary canards near
resonance.Comment: To appear in SIAM Journal of Applied Dynamical System
Codimension three bifurcation of streamline patterns close to a no-slip wall: A topological description of boundary layer eruption
Painting the Palace of Apries I: ancient binding media and coatings of the reliefs from the Palace of Apries, Lower Egypt
This study gives an account of the organic components (binders and coatings) found in the polychromy of some fragmented architectural reliefs from the Palace of Apries in Memphis, Egypt (26th Dynasty, ca. 589-568 BCE). A column capital and five relief fragments from the collections of the Ny Carlsberg Glyptotek in Copenhagen were chosen for examination, selected because of their well-preserved polychromy. Samples from the fragments were first investigated using Fourier transform infrared (FTIR) spectroscopy to screen for the presence of organic materials and to identify the chemical family to which these materials belong (proteinaceous, polysaccharides or lipid). Only the samples showing the potential presence of organic binder residues were further investigated using gas chromatography with mass spectrometry detection (GC-MS) targeting the analysis towards the detection and identification of compounds belonging to the chemical families identified by FTIR. The detection of polysaccharides in the paint layers on the capital and on two of the fragments indicates the use of plant gums as binding media. The interpretation of the sugar profiles was not straightforward so botanical classification was only possible for one fragment where the results of analysis seem to point to gum arabic. The sample from the same fragment was found to contain animal glue and a second protein material (possibly egg). While the presence of animal glue is probably ascribable to the binder used for the ground layer, the second protein indicates that either the paint layer was bound in a mixture of different binding materials or that the paint layer, bound in a plant gum, was then coated with a proteinaceous material. The surface of two of the investigated samples was partially covered by translucent waxy materials that were identified as a synthetic wax (applied during old conservation treatments) and as beeswax, respectively. It is possible that the beeswax is of ancient origin, selectively applied on yellow areas in order to create a certain glossiness or highlight specific elements
Leukocyte telomere length is associated with elevated plasma glucose and HbA1c in young healthy men independent of birth weight.
Telomeres are protein-bound regions of repetitive nucleotide sequences (TTAGGG) at the end of human chromosomes, and their length is a marker of cellular aging. Intrauterine growth restriction is associated with shorter blood cell telomeres at birth and individuals with type 2 diabetes have shorter telomeres. Individuals with a low birth weight (LBW) have an increased risk of metabolic disease and type 2 diabetes. Therefore, we aimed to investigate the relationship between birth weight and telomere length and the association between birth weight, telomere length and cardiometabolic phenotype in adulthood. Young, healthy men with LBW (n = 55) and normal birth weight (NBW) (n = 65) were examined including blood pressure, blood samples and body composition. Leukocyte telomere length was determined using a high-throughput qPCR method. The LBW men were more insulin resistant as determined by the HOMA-IR index. There was no difference in telomere length between LBW and NBW subjects. When adjusting for birth weight and cohort effect, significant negative associations between telomere length and fasting glucose (P = 0.003) and HbA1c (P = 0.0008) were found. In conclusion, no significant difference in telomere length was found between LBW and NBW men. The telomere length was negatively associated with glucose concentrations and HbA1c levels within the normal non-diabetic range independent of birth weight
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