Analytic invariants associated with a parabolic fixed point in C2

It is well known that in a small neighbourhood of a parabolic fixed point a real-analytic diffeomorphism of (R2,0) embeds in a smooth autonomous flow. In this paper we show that the complex-analytic situation is completely different and a generic diffeomorphism cannot be embedded in an analytic flow in a neighbourhood of its parabolic fixed point. We study two analytic invariants with respect to local analytic changes of coordinates. One of the invariants was introduced earlier by one of the authors. These invariants vanish for time-one maps of analytic flows. We show that one of the invariants does not vanish on an open dense subset. A complete analytic classification of the maps with a parabolic fixed point in C2 is not available at the present time

A Predator-Prey Model with Non-Monotonic Response Function

We study the dynamics of a family of planar vector fields that models certain populations of predators and their prey. This model is adapted from the standard Volterra-Lotka system by taking into account group defense, competition between prey and competition between predators. Also we initiate computer-assisted research on time-periodic perturbations, which model seasonal dependence. We are interested in persistent features. For the planar autonomous model this amounts to structurally stable phase portraits. We focus on the attractors, where it turns out that multi-stability occurs. Further, we study the bifurcations between the various domains of structural stability. It is possible to fix the values of two of the parameters and study the bifurcations in terms of the remaining three. We find several codimension 3 bifurcations that form organizing centers for the global bifurcation set. Studying the time-periodic system, our main interest is the chaotic dynamics. We plot several numerical examples of strange attractors

Linearization of germs of hyperbolic vector fields

We develop a normal form to express asymptotically a conjugacy between a germ of resonant vector field and its linear part. We show that such an asymptotic expression can be written in terms of functions of the Logarithmic Mourtada type. To cite this article: P Bonckaert et al., C. R. Acad. Sci. Paris, Ser. I336 (2003). (C) 2003 Academie des sciences/Editions scientifiques et medicales Elsevier SAS. All rights reserved.MathematicsSCI(E)0ARTICLE119-2233

Caractérisation par imagerie en temps réel de cultures cellulaires hépatiques en biopuces microfluidiques

Le développement de méthodes alternatives à la culture in vivo pour l évaluation de la toxicité des molécules chimiques s est accéléré ces dernières années, l objectif étant de limiter l utilisation d animaux. Préconisés par l OCDE (Organisation de coopération et de développement économiques), ces modèles alternatifs visent à mimer les conditions physiologiques en employant des systèmes in vitro ou in silico. Parmi les différents systèmes développés, les biopuces microfluidiques ont prouvé leur contribution à l amélioration des fonctions cellulaires, ce qui permet des études toxicologiques pertinentes. Les travaux de ce doctorat sont basés sur l emploi de ces biopuces pour cultiver des hépatocytes (cellules du foie) et portent sur la mise au point d une méthode d analyse d images issues de ces cultures sous microscope au cours du temps. L acquisition d images tout au long de l expérience permet de suivre, après traitement, l évolution et le comportement des cellules au contact de molécules chimiques et d évaluer les réponses toxicologiques. Les premiers résultats de ces travaux ont permis l amélioration du procédé de culture microfluidique adaptée au matériel d acquisition d images, la sélection de sondes fluorescentes, et le choix d un algorithme de traitement des images sur CellProfiler. Cela nous a permis de quantifier et caractériser certaines fonctions biologiques au sein de la biopuce comme l activité mitochondriale. Le potentiel de cet outil pour évaluer la toxicité de molécule a été testé grâce à l emploi d un toxique connu : la staurosporine. Les résultats obtenus ont révélé l impact de la mise en culture en dynamique sur le comportement des hépatocytes, et la toxicité de la staurosporine visible en biopuce.The development of alternative methods of in vivo cultures for the toxicological evaluation of chemical molecules has accelerated this last years, in order to limit the use of animals. Recommended by the OECD (Organisation for Economic Cooperation and Development), these alternative models are designed to mimic the physiological conditions using in vitro or in silico systems. Among the developed systems, microfluidic biochips have proven their contribution to the improvement of cellular functions, which allows relevant toxicological studies. This PhD thesis is based on the use of these biochips for hepatocytes culture and focus on the development of an analysis method for study these cultures under microscope over time using imaging. Image acquisition throughout the experiment enables to analyze, after image processing, the evolution and the behavior of cells in contact with chemical molecules and to evaluate toxicological responses. The first results of this work led to the optimization of the microfluidic cultures under the microscope used to get the image sequences, the selection of fluorescent probes and the development of an image processing system with CellProfiler. These works allowed the quantification and the characterization of some biological functions within the biochip such as the mitochondrial activity. Staurosporine, a well-known toxic, has been used to test the potential of this tool to evaluate the toxicity of molecules. The results showed the impact of dynamic culture on the hepatocytes behavior, and the staurosporine toxicity, in biochip cultures.COMPIEGNE-BU (601592101) / SudocSudocFranceF

Homoclinic Bifurcations for the Henon Map

Chaotic dynamics can be effectively studied by continuation from an anti-integrable limit. We use this limit to assign global symbols to orbits and use continuation from the limit to study their bifurcations. We find a bound on the parameter range for which the Henon map exhibits a complete binary horseshoe as well as a subshift of finite type. We classify homoclinic bifurcations, and study those for the area preserving case in detail. Simple forcing relations between homoclinic orbits are established. We show that a symmetry of the map gives rise to constraints on certain sequences of homoclinic bifurcations. Our numerical studies also identify the bifurcations that bound intervals on which the topological entropy is apparently constant.Comment: To appear in PhysicaD: 43 Pages, 14 figure